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Wyświetlanie 1-15 z 53
Tytuł:
Positive solution of a fractional differential equation with integral boundary conditions
Autorzy:
Abdo, M. S.
Wahash, H. A.
Panchal, S. K.
Powiązania:
https://bibliotekanauki.pl/articles/122788.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional derivative and integral
positive solutions of nonlinear boundary value problems
upper and lower solutions
fixed point theorem
pochodna ułamkowa
twierdzenie o punkcie stałym
twierdzenia o punkcie stałym Schaudera
równania różniczkowe cząstkowe
nieliniowe cząstkowe równanie różniczkowe
zagadnienie brzegowe
Opis:
In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 5-15
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiple solutions of boundary value problems on time scales for φ-laplacian operator
Autorzy:
Amster, Pablo
Kuna, Mariel Paula
Santos, Dionicio Pastor
Powiązania:
https://bibliotekanauki.pl/articles/255690.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
dynamic equations on time scales
nonlinear boundary value problems
upper and lower solutions
Leray-Schauder degree
multiple solutions
Opis:
We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete p-Laplacian as well as those for boundary value problems on time scales.
Źródło:
Opuscula Mathematica; 2020, 40, 4; 405-425
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
Autorzy:
Auzinger, W.
Karner, E.
Koch, O.
Weinmuller, E.
Powiązania:
https://bibliotekanauki.pl/articles/255635.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
polynomial collocation
singular boundary value problems
linear and nonlinear eigenvalue problems
Opis:
We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 229-241
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side
Autorzy:
Averna, Diego
Bonanno, Gabriele
Powiązania:
https://bibliotekanauki.pl/articles/1294053.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
multivalued differential inclusions
boundary value problems
non-convex and unbounded right-hand side
directional continuous selections
implicit equations
Opis:
Let $F:[a,b] × ℝ^n × ℝ^n → 2^{ℝ^n}$ be a multifunction with possibly non-convex and unbounded values. The main result of this paper (Theorem 1) asserts that, given the multivalued boundary value problem ($P_F$)    {u'' ∈ F(t,u,u'), u(a) = u(b) = ϑ_{ℝ^n}, if an appropriate restriction of the multifunction F has non-empty and closed values and satisfies the lower Scorza Dragoni property and a weak integrable boundedness type condition, then we can substitute the problem ($P_F$) with another one ($P_G$), with a suitable convex right-hand side G, such that every generalized solution of ($P_G$) is also a generalized solution of ($P_F$) (see also Remark 1 and Corollary 1). As a consequence of our results, in conjunction with those in [13] and [18], some existence theorems for multivalued boundary value problems are then presented (see Theorem 2, Corollary 2 and Theorem 3). Finally, some applications are given to the existence of generalized solutions for two implicit boundary value problems (Theorems 4-6).
Źródło:
Annales Polonici Mathematici; 1999, 71, 3; 253-271
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence results for delay second order differential inclusions
Autorzy:
Azzam-Laouir, Dalila
Haddad, Tahar
Powiązania:
https://bibliotekanauki.pl/articles/729461.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
boundary-value problems
delay differential inclusions
fixed point
retract
Opis:
In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2008, 28, 1; 133-146
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial-boundary value problems for impulsive parabolic functional differential equations
Autorzy:
Bainov, D.
Kamont, Zdzisław
Minchev, E.
Powiązania:
https://bibliotekanauki.pl/articles/1339288.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
initial-boundary value problems
impulsive parabolic equations
Opis:
Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 1-15
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Superlinear elliptic systems with distributed and boundary controls
Autorzy:
Bors, D.
Powiązania:
https://bibliotekanauki.pl/articles/970975.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
zagadnienie brzegowe
stabilność
metoda wariacyjna
boundary value problems
continuous dependence
stability
variational methods
Opis:
The paper investigates the nonlinear partial differential equations of the superlinear elliptic type with the Dirichlet boundary data. Some sufficient conditions, under which the solutions of considered equations depend continuously on distributed and boundary controls, are proved. The proofs of the main results are based on variational methods.
Źródło:
Control and Cybernetics; 2005, 34, 4; 987-1004
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An Influence of the Wall Acoustic Impedance on the Room Acoustics. The Exact Solution
Autorzy:
Brański, A.
Kocan-Krawczyk, A.
Prędka, E.
Powiązania:
https://bibliotekanauki.pl/articles/177084.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
Fourier analysis
architectural acoustics
absorption coefficients
boundary-value problems
Opis:
The Fourier method is applied to the description of the room acoustics field with the combination of uniform impedance boundary conditions imposed on some walls. These acoustic boundary conditions are expressed by absorption coefficient values In this problem, the Fourier method is derived as the combination of three one-dimensional Sturm-Liouville (S-L) problems with Robin-Robin boundary conditions at the first and second dimension and Robin-Neumann ones at the third dimension. The Fourier method requires an evaluation of eigenvalues and eigenfunctions of the Helmholtz equation, via the solution of the eigenvalue equation, in all directions. The graphic-analytical method is adopted to solve it It is assumed that the acoustic force constitutes a monopole source and finally the forced acoustic field is calculated. As a novelty, it is demonstrated that the Fourier method provides a useful and efficient approach for a room acoustics with different values of wall impedances. Theoretical considerations are illustrated for rectangular cross-section of the room with particular ratio. Results obtained in the paper will be a point of reference to the numerical calculations.
Źródło:
Archives of Acoustics; 2017, 42, 4; 677-687
0137-5075
Pojawia się w:
Archives of Acoustics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The numerical solution of nonlinear two-point boundary value problems using iterated deferred correction - a survey
Autorzy:
Cash, J. R.
Powiązania:
https://bibliotekanauki.pl/articles/255625.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
deferred correction
boundary value problems
conditioning
mesh selection
Opis:
The use of iterated deferred correction has proved to be a very efficient approach to the numerical solution of general first order systems of nonlinear two-point boundary value problems. In particular the two high order codes TWPBVP.f, based on mono-implicit Runge-Kutta (MIRK) formulae, and TWPBVPL.f based on Lobatto Runge-Kutta formulae as well as the continuation codes ACDC.f and COLMOD.f are now widely used. In this survey we describe some of the problems involved in the derivation of efficient deferred correction schemes. In particular we consider the construction of high order methods which preserve the stability of the underlying formulae, the choice of the mesh choosing algorithm which is based both on local accuracy and conditioning, and the computation of continuous solutions.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 269-287
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities
Autorzy:
Chidouh, A.
Torres, D. F. M.
Powiązania:
https://bibliotekanauki.pl/articles/255913.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional difference equations
Lyapunov-type inequalities
fractional boundary value problems
positive solutions
Opis:
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
Źródło:
Opuscula Mathematica; 2018, 38, 1; 31-40
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a semilinear elliptic eigenvalue problem
Autorzy:
Coclite, Mario
Powiązania:
https://bibliotekanauki.pl/articles/1294623.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
semilinear elliptic equations
nonlinear boundary-value problems
positive solutions
supersolution and subsolution method
Opis:
We obtain a description of the spectrum and estimates for generalized positive solutions of -Δu = λ(f(x) + h(u)) in Ω, $u|_{∂Ω} = 0$, where f(x) and h(u) satisfy minimal regularity assumptions.
Źródło:
Annales Polonici Mathematici; 1997, 67, 3; 289-295
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reconstruction of potential and boundary conditions for second order difference equations
Autorzy:
Currie, Sonja
Love, Anne
Powiązania:
https://bibliotekanauki.pl/articles/962820.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Difference equations
inverse problem
boundary value problems
potential
eigenvalues
Opis:
Assume the eigenvalues and the weights are given for a difference boundary value problem and that the form of the boundary conditions at the endpoints is known. In particular, it is known whether the endpoints are fixed (i.e. Dirichlet or non-Dirichlet boundary conditions) or whether the endpoints are free to move (i.e. boundary conditions with affine dependence on the eigenparameter). This work illustrates how the potential as well as the exact boundary conditions can be uniquely reconstructed. The procedure is inductive on the number of unit intervals. This paper follows along the lines of S. Currie and A. Love, Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions, \emph{Quaestiones Mathematicae}, 40 (2017), no. 7, 861−877. Since the inverse problem considered in this paper contains more unknowns than the inverse problem considered in the above reference, an additional spectrum is required more often than was the case in the unique reconstruction of the potential alone.
Źródło:
Commentationes Mathematicae; 2018, 58, 1-2; 1-9
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized solutions of first order partial differential functional inequalities
Autorzy:
Czernous, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/746208.pdf
Data publikacji:
2006
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
initial boundary value problems
partial functional differential inequalities
Carathéodory solutions
uniqueness
bicharacteristics
Opis:
The paper deals with initial boundary value problems for nonlinear first order partial differential functional equations. A theorem on the uniqueness of generalized solutions is proved. It is based on a comparison result for functional differential inequalities in the Carathéodory sense. A theorem on generalized solutions of functional differential inequalities is presented.
Źródło:
Commentationes Mathematicae; 2006, 46, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analytical solution of mixed boundary value problems using the displacement potential approach for the case of plane stress and plane strain conditions
Autorzy:
Deb Nath, S. K.
Powiązania:
https://bibliotekanauki.pl/articles/266247.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
rozwiązanie analityczne
naprężenie płaskie
odkształcenie
wartość graniczna
analytical solution
displacement potential approach
plane stress and plane strain conditions
mixed boundary value problems
Opis:
Two elastic plate problems made of duralumin are solved analytically using the displacement potential approach for the case of plane strain and plane stress conditions. Firstly, a one end fixed plate is considered in which the rest of the edges are stiffened and a uniform load is applied to the opposite end of the fixed end. Secondly, a plate is considered in which all of the edges are stiffened and a uniform tension is applied at its both ends. Solutions to both of the problems are presented for the case of plane stress and plane strain conditions. The effects of plane stress and plane strain conditions on the solutions are explained. In the case of stiffening of the edges of the plate, the shape of the plate does not change abruptly, which is clearly observed in both of the cases. For the plane strain condition, the plates become stiffer in the loading direction as compared to the plane stress condition. For the plane strain condition, there is a significant variation of the normal stress component, σzz at different sections of the plate. The graphical results, clearly identify the critical regions of the plate for the case of the plane stress and plane strain condition.
Źródło:
International Journal of Applied Mechanics and Engineering; 2017, 22, 2; 269-291
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
Autorzy:
El Amrouss, Abdelrachid
Hammouti, Omar
Powiązania:
https://bibliotekanauki.pl/articles/2051984.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
discrete boundary value problems
2n-th order
variational methods
critical point theory
Opis:
Let $n \in N^{\star}$, and $N \geq n$ be an integer. We study the spectrum of discrete linear $2n$-th order eigenvalue problems \[ \begin{cases} \Sigma_{k=0}^{n}(-1)^{k} \Delta^{2k} u(t-k) = \lambda{}u(t), & t \in[1,N]_{\mathbb{Z}} \\ \Delta^{i}u(-(n-1)) = \Delta^{i}u(N-(n-1)), & i \in[0, 2n-1]_{\mathbb{Z}} \end{cases} \] where A is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear $2n$-th order problems by applying the variational methods and critical point theory.
Źródło:
Opuscula Mathematica; 2021, 41, 4; 489-507
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 53

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