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Wyświetlanie 1-15 z 16
Tytuł:
Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions
Autorzy:
Wang, Ming-Xing
Cabada, Alberto
Nieto, Juan
Powiązania:
https://bibliotekanauki.pl/articles/1311755.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
upper and lower solutions
monotone iterative technique
Carathéodory function
Opis:
The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.
Źródło:
Annales Polonici Mathematici; 1993, 58, 3; 221-235
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On boundary value problems of second order differential inclusions
Autorzy:
Dhage, Bapur
Powiązania:
https://bibliotekanauki.pl/articles/729619.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusion
method of upper and lower solutions
existence theorem
Opis:
This paper presents sufficient conditions for the existence of solutions to boundary-value problems of second order multi-valued differential inclusions. The existence of extremal solutions is also obtained under certain monotonicity conditions.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 73-96
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The method of upper and lower solutions for perturbed nth order differential inclusions
Autorzy:
Dhage, Bupurao
Petruşel, Adrian
Powiązania:
https://bibliotekanauki.pl/articles/729580.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusion
method of upper and lower solutions
existence theorem
Opis:
In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2006, 26, 1; 57-76
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the existence of five nontrivial solutions for resonant problems with p-Laplacian
Autorzy:
Gasiński, Leszek
Papageorgiou, Nikolaos
Powiązania:
https://bibliotekanauki.pl/articles/729275.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
p-Laplacian
Clarke subdifferential
linking sets
upper-lower solutions
second eigenvalue
nodal and constant sign solutions
second deformation theorem
Opis:
In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of $(-Δₚ,W₀^{1,p}(Z))$. We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 169-189
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Upper and lower solutions satisfying the inverse inequality
Autorzy:
Rachůnková, Irena
Powiązania:
https://bibliotekanauki.pl/articles/1310660.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
existence
multipoint and two-point BVP
upper and lower solutions
topological degree
Opis:
We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.
Źródło:
Annales Polonici Mathematici; 1996-1997, 65, 3; 235-244
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions
Autorzy:
R., D.
Wang, Haiyan
Powiązania:
https://bibliotekanauki.pl/articles/1294312.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
nonlinear boundary value problems
multiplicity of positive solutions
upper and lower solutions
degree theory
Opis:
We study the existence and multiplicity of positive solutions of the nonlinear equation u''(x) + λh(x)f(u(x)) = 0 subject to nonlinear boundary conditions. The method of upper and lower solutions and degree theory arguments are used.
Źródło:
Annales Polonici Mathematici; 1998, 69, 2; 155-165
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Impulsive functional-differential equations of first order
Autorzy:
Skóra, Lidia
Powiązania:
https://bibliotekanauki.pl/articles/744828.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
impulsive functional-differential equation
Volltera operator
upper and lower solutions
monotone iterative technique
global solutions
Opis:
In this paper we present some existence results for impulsive functional-differential equations of first order.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions
Autorzy:
Gao, Wenjie
Wang, Junyu
Powiązania:
https://bibliotekanauki.pl/articles/1311418.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
two-point boundary value problems
upper and lower solutions
Nagumo condition
existence
Carathéodory functions
Opis:
The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].
Źródło:
Annales Polonici Mathematici; 1995, 62, 3; 283-291
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Quasilinearization method for finite systems of nonlinear RL fractional differential equations
Autorzy:
Denton, Zachary
Ramirez, Juan Diego
Powiązania:
https://bibliotekanauki.pl/articles/1397341.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
lower and upper solutions
quasilinearization method
Opis:
In this paper the quasilinearization method is extended to finite systems of Riemann-Liouville fractional differential equations of order 0 < q < 1. Existence and comparison results of the linear Riemann-Liouville fractional differential systems are recalled and modified where necessary. Using upper and lower solutions, sequences are constructed that are monotonic such that the weighted sequences converge uniformly and quadratically to the unique solution of the system. A numerical example illustrating the main result is given.
Źródło:
Opuscula Mathematica; 2020, 40, 6; 667-683
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A generalized periodic boundary value problem for the one-dimensional p-Laplacian
Autorzy:
Jiang, Daqing
Wang, Junyu
Powiązania:
https://bibliotekanauki.pl/articles/1310724.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
generalized periodic boundary value problem
p-Laplacian
upper and lower solutions
Carathéodory function
Nagumo condition
Opis:
The generalized periodic boundary value problem -[g(u')]' = f(t,u,u'), a < t < b, with u(a) = ξu(b) + c and u'(b) = ηu'(a) is studied by using the generalized method of upper and lower solutions, where ξ,η ≥ 0, a, b, c are given real numbers, $g(s) = |s|^{p-2} s$, p > 1, and f is a Carathéodory function satisfying a Nagumo condition. The problem has a solution if and only if there exists a lower solution α and an upper solution β with α(t) ≤ β(t) for a ≤ t ≤ b.
Źródło:
Annales Polonici Mathematici; 1996-1997, 65, 3; 265-270
0066-2216
Pojawia się w:
Annales Polonici Mathematici
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:
Monotone iterative technique for finite systems of nonlinear Riemann-,Lliouville fractional differential equations
Autorzy:
Denton, Z.
Vatsala, A.S.
Powiązania:
https://bibliotekanauki.pl/articles/255746.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
coupled lower and upper solutions
mixed quasimonotone property
Opis:
Comparison results of the nonlinear scalar Riemann-Liouville fractional differential equation of order q, 0 < q ≤ 1, are presented without requiring Hölder continuity assumption. Monotone method is developed for finite systems of fractional differential equations of order q, using coupled upper and lower solutions. Existence of minimal and maximal solutions of the nonlinear fractional differential system is proved.
Źródło:
Opuscula Mathematica; 2011, 31, 3; 327-339
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone method for Riemann-Liouville multi-order fractional differential systems
Autorzy:
Denton, Z.
Powiązania:
https://bibliotekanauki.pl/articles/254754.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential systems
multi-order systems
lower and upper solutions
monotone method
Opis:
In this paper we develop the monotone method for nonlinear multi-order N-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders qi where 0 < qi < 1. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
Źródło:
Opuscula Mathematica; 2016, 36, 2; 189-206
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extremal solutions to a coupled system of nonlinear fractional differential equations with Caputo fractional derivatives
Autorzy:
Derbazi, Choukri
Baitiche, Zidane
Benchohra, Mouffak
Graef, John R.
Powiązania:
https://bibliotekanauki.pl/articles/2052385.pdf
Data publikacji:
2021
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
Caputo fractional derivative
coupled system
extremal solutions
monotone iterative technique
upper and lower solutions
pochodna ułamkowa Caputo
system sprzężony
ekstremalne rozwiązania
monotoniczna technika iteracyjna
Opis:
Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the $\psi$-Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.
Źródło:
Journal of Mathematics and Applications; 2021, 44; 19-34
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:
Brzychczy, S.
Powiązania:
https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
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