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Wyświetlanie 1-25 z 43
Tytuł:
Multiplicity results for perturbed fourth-order Kirchhoff-type problems
Autorzy:
Tavani, M. R. H.
Afrouzi, G. A.
Heidarkhani, S.
Powiązania:
https://bibliotekanauki.pl/articles/952853.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multiplicity results
multiple solutions
fourth-order Kirchhoff-type equation
variational methods
critical point theory
Opis:
In this paper, we investigate the existence of three generalized solutions for fourth-order Kirchhoff-type problems with a perturbed nonlinear term depending on two real parameters. Our approach is based on variational methods.
Źródło:
Opuscula Mathematica; 2017, 37, 5; 755-772
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear eigenvalue problems for fourth order ordinary differential equations
Autorzy:
Przybycin, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/1311640.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
bifurcation point
bifurcation interval
Leray-Schauder degree
characteristic value
Opis:
This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of Rabinowitz ([5], [6]) is not applicable here. We use the properties of Leray-Schauder degree to establish the existence of nontrivial solutions and describe their location. The results obtained are similar to those proved by Chiappinelli for Sturm-Liouville operators.
Źródło:
Annales Polonici Mathematici; 1994-1995, 60, 3; 249-253
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Linear differential equations of second, third, and fourth order
Autorzy:
Hernández-Galeana, A.
López-Bonilla, J.
López-Vázquez, R.
Vidal-Beltrán, S.
Powiązania:
https://bibliotekanauki.pl/articles/1167198.pdf
Data publikacji:
2018
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Abel-Liouville-Ostrogradski identity
Euler-Lagrange method
Linear differential equation
Opis:
We study the linear differential equations of second, third, and fourth order, accepting to know solutions of the corresponding homogeneous equation, then we show how to obtain one more solution for the homogeneous case and a particular solution for the original equation.
Źródło:
World Scientific News; 2018, 105; 225-232
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory properties of fourth order nonlinear difference equations with quasidifferences
Autorzy:
Schmeidel, E.
Migda, M.
Musielak, A.
Powiązania:
https://bibliotekanauki.pl/articles/255808.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
nonlinear difference equation
oscillatory solution
nonoscillatory solution
fourth order
Opis:
In this paper we present the oscillation criterion for a class of fourth order nonlinear difference equations with quasidifferences.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 371-380
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An optimal control problem for a fourth-order variational inequality
Autorzy:
Khludnev, A.
Powiązania:
https://bibliotekanauki.pl/articles/1361143.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:
An optimal control problem is considered where the state of the system is described by a variational inequality for the operator w → εΔ²w - φ(‖∇w‖²)Δw. A set of nonnegative functions φ is used as a control region. The problem is shown to have a solution for every fixed ε > 0. Moreover, the solvability of the limit optimal control problem corresponding to ε = 0 is proved. A compactness property of the solutions of the optimal control problems for ε > 0 and their relation with the limit problem are established. This type of operator arises in the theory of nonlinear plates, and the choice of a most suitable function φ is of interest for applications [2]. The problem of control of the function w has been studied in [4] for the operator under consideration, and some statements of this work will be used. Nonstationary problems with analogous operators were analyzed in [6,7]. Some general results on control of second-order variational inequalities can be found in [1]. The first section of this paper deals with the control problem for our fourth-order operator, the second considers a second-order operator, and the third studies the relationship between the solutions of the two problems.
Źródło:
Banach Center Publications; 1992, 27, 1; 225-231
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and uniqueness theorems for fourth-order boundary value problems
Autorzy:
Przybycin, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/1294726.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
eigenvalue
Leray-Schauder degree
Fredholm alternative
Opis:
We establish the existence and uniqueness theorems for a linear and a nonlinear fourth-order boundary value problem. The results obtained generalize the results of Usmani [4] and Yang [5]. The methods used are based, in principle, on [3], [5].
Źródło:
Annales Polonici Mathematici; 1997, 67, 1; 59-64
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a fourth order discrete boundary value problem
Autorzy:
Galewski, M.
Smejda, J.
Powiązania:
https://bibliotekanauki.pl/articles/255355.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
discrete boundary value problem
variational method
coercivity
continuous dependence on paremeters
Opis:
Using variational methods we investigate the existence of solutions and their dependence on parameters for certain fourth order difference equations.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 115-123
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weakly Bound States in Heterogeneous Waveguides: A Calculation to Fourth Order
Autorzy:
Amore, P.
Powiązania:
https://bibliotekanauki.pl/articles/1032586.pdf
Data publikacji:
2017-10
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
trapped modes
bound states
deformed waveguide
perturbation theory
Opis:
We have extended a previous calculation of the energy of a weakly heterogeneous waveguide to fourth order in the density perturbation, deriving its general expression. For particular configurations where the second and third orders both vanish, we discover that the fourth order contribution lowers in general the energy of the state, below the threshold of the continuum. In these cases the waveguide possesses a localized state. We have applied our general formula to a solvable model with vanishing second and third orders reproducing the exact expression for the fourth order.
Źródło:
Acta Physica Polonica A; 2017, 132, 4; 1351-1357
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On attaining the prescribed quality of a controlled fourth order system
Autorzy:
Kapustyan, V.
Maksimov, V.
Powiązania:
https://bibliotekanauki.pl/articles/329889.pdf
Data publikacji:
2014
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
auxiliary model
feedback control
online reconstruction
model pomocniczy
sprzężenie zwrotne
rekonstrukcja
Opis:
In this paper, we discuss a method of auxiliary controlled models and its application to solving some robust control problems for a system described by differential equations. As an illustration, a system of nonlinear differential equations of the fourth order is used. A solution algorithm, which is stable with respect to informational noise and computational errors, is presented. The algorithm is based on a combination of online state/input reconstruction and feedback control methods.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2014, 24, 1; 75-85
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical scheme for time-fractional fourth-order reaction-diffusion model
Autorzy:
Koç, Dilara Altan
Powiązania:
https://bibliotekanauki.pl/articles/24201500.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
implicit finite difference method
fractional calculus
diffusion equation
niejawna metoda różnic skończonych
rachunek ułamkowy
równanie dyfuzji
Opis:
In fractional calculus, the fractional differential equation is physically and theoretically important. In this article an efficient numerical process has been developed. Numerical solutions of the time fractional fourth order reaction diffusion equation in the sense of Caputo derivative is obtained by using the implicit method, which is a finite difference method and is developed by increasing the number of iterations. The advantage of the implicit difference scheme is unconditionally stable. The stability analysis and convergency have been proven. A numerical example has been presented, and the validity of the method is supported by tables and graphics.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 15--25
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Oscillatory properties of solutions of the fourth order difference equations with quasidifferences
Autorzy:
Jankowski, R.
Schmeidel, E.
Zonenberg, J.
Powiązania:
https://bibliotekanauki.pl/articles/255677.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fourth-order difference equation
neutral type
quickly oscillatory solutions
almost oscillatory
Opis:
A class of fourth-order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four-dimensional difference system. The sufficient conditions under which the considered equation has no quickly oscillatory solutions are given. Finally, the sufficient conditions under which the equation is almost oscillatory are presented.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 789-797
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiple positive solutions of a nonlinear fourth order periodic boundary value problem
Autorzy:
Kong, Lingbin
Jiang, Daqing
Powiązania:
https://bibliotekanauki.pl/articles/1294291.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear periodic boundary value problem
multiple positive solutions
cone
fixed point index
Opis:
The fourth order periodic boundary value problem $u^{(4)} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^{(i)}(0) = u^{(i)}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^{-7}$.
Źródło:
Annales Polonici Mathematici; 1998, 69, 3; 265-270
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The fourth-order ordinary differential equation with the fractional initial/boundary conditions
Autorzy:
Siedlecki, Jarosław
Powiązania:
https://bibliotekanauki.pl/articles/122929.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional calculus
ordinary differential equation
analytical solution
rachunek ułamkowy
równanie różniczkowe zwyczajne
rozwiązanie analityczne
warunek brzegowy
Opis:
The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 79-87
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiple solutions for fourth order elliptic problems with p(x)-biharmonic operators
Autorzy:
Kong, L.
Powiązania:
https://bibliotekanauki.pl/articles/254793.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
critical points
p(x)-biharmonic operator
weak solutions
mountain pass lemma
Opis:
We study the multiplicity of weak solutions to the following fourth order nonlinear elliptic problem with a p(x)-biharmonic operator [formula] where Ω is a smooth bounded domain in RN, [formula] is the p(x)-biharmonic operator, and λ > 0 is a parameter. We establish sufficient conditions under which there exists a positive number λ* such that the above problem has at least two nontrivial weak solutions for each λ > λ*. Our analysis mainly relies on variational arguments based on the mountain pass lemma and some recent theory on the generalized Lebesgue-Sobolev spaces [formula].
Źródło:
Opuscula Mathematica; 2016, 36, 2; 253-264
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The fourth-order ordinary differential equation with the fractional initial/boundary conditions
Autorzy:
Siedlecki, Jarosław
Powiązania:
https://bibliotekanauki.pl/articles/1839799.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional calculus
ordinary differential equation
analytical solution
rachunek ułamkowy
równanie różniczkowe zwyczajne
rozwiązanie analityczne
warunek brzegowy
Opis:
The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 79-87
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the estimate of the fourth-order homogeneous coefficient functional for univalent functions
Autorzy:
Gromova, Larisa
Vasil'ev, Alexander
Powiązania:
https://bibliotekanauki.pl/articles/1311241.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
univalent function
area method
Opis:
The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions $f(z) = z + ∑^{∞}_{n=2} c_n z^n$ in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.
Źródło:
Annales Polonici Mathematici; 1996, 63, 1; 7-12
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
Autorzy:
Przybycin, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/1312084.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear partial differential equations
bifurcation in partial differential equations
Opis:
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar to those proved by Rabinowitz for second order elliptic partial differential equations ([5]-[7]). The methods used are based, in principle, on the results of [1], [5], [6].
Źródło:
Annales Polonici Mathematici; 1992, 57, 1; 21-28
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations
Autorzy:
Yanbing, Yang
Ahmed, Md Salik
Lanlan, Qin
Runzhang, Xu
Powiązania:
https://bibliotekanauki.pl/articles/255961.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fourth-order nonlinear wave equation strong damping
blow up
global existence
Opis:
Global well-posedness and finite time blow up issues for some strongly damped nonlinear wave equation are investigated in the present paper. For subcritical initial energy by employing the concavity method we show a finite time blow up result of the solution. And for critical initial energy we present the global existence, asymptotic behavior and finite time blow up of the solution in the framework of the potential well. Further for supercritical initial energy we give a sufficient condition on the initial data such that the solution blows up in finite time.
Źródło:
Opuscula Mathematica; 2019, 39, 2; 297-313
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Boundary integral solution for a class of fourth-order two-point boundary value problems
Autorzy:
Al-Gahtani, H. J.
Powiązania:
https://bibliotekanauki.pl/articles/122949.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
boundary integral method
fourth-order differential equation
nonlinear ordinary differential equations
nieliniowe równania różniczkowe zwyczajne
równanie różniczkowe czwartego rzędu
Opis:
In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation yiv+P(x, y, y’, y’’, y’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 5-13
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Blowup phenomena for some fourth-order strain wave equations at arbitrary positive initial energy level
Autorzy:
Lin, Qiang
Luo, Yongbing
Powiązania:
https://bibliotekanauki.pl/articles/2048896.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fourth-order strain wave equation
arbitrary positive initial energy
blowup
blowup time
Opis:
In this paper, we study a series of fourth-order strain wave equations involving dissipative structure, which appears in elasto-plastic-microstructure models. By some differential inequalities, we derive the finite time blow up results and the estimates of the upper bound blowup time with arbitrary positive initial energy. We also discuss the influence mechanism of the linear weak damping and strong damping on blowup time, respectively.
Źródło:
Opuscula Mathematica; 2022, 42, 2; 219-238
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-25 z 43

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