Results 11 to 20 of about 57 (56)

Method of semidiscretization in time for quasilinearintegrodifferential equations

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 9, Page 469-478, 2004., 2004
We consider a class of quasilinear integrodifferential equations in a reflexive Banach space. We apply the method of semidiscretization in time to establish the existence, uniqueness, and continuous dependence on the initial data of strong solutions.
D. Bahuguna, Reeta Shukla
wiley   +1 more source

Method of semidiscretization in time to nonlinear retarded differential equations with nonlocal history conditions

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 37, Page 1943-1956, 2004., 2004
This paper deals with the applications of the method of semidiscretization in time to a nonlinear retarded differential equation with a nonlocal history condition. We establish the existence and uniqueness of a strong solution. Finally, we consider some applications of the abstract results.
S. Agarwal, D. Bahuguna
wiley   +1 more source

Monotone iterative technique for non-autonomous semilinear differential equations with nonlocal condition

Demonstratio Mathematica, 2019
The objective of this article is to discuss the existence and uniqueness of mild solutions for a class of non-autonomous semilinear differential equations with nonlocal condition via monotone iterative method with upper and lower solutions in an ordered ...
Meraj Arshi, Pandey Dwijendra Narain
doaj   +1 more source

Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations

International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 213-219, 2004., 2004
In the present work, we consider a semilinear retarded differential equation in a Banach space. We first establish the existence and uniqueness of a mild solution and then prove its regularity under different additional conditions. Finally, we consider some applications of the abstract results.
D. Bahuguna
wiley   +1 more source

On a nonlocal Cauchy problem for differential inclusions

Abstract and Applied Analysis, Volume 2004, Issue 5, Page 425-434, 2004., 2004
We establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed‐point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer′s fixed‐point theorem combined with lower semicontinuous multivalued operators with decomposable values.
E. Gatsori, S. K. Ntouyas, Y. G. Sficas
wiley   +1 more source

Multivalued semilinear neutral functional differential equations with nonconvex‐valued right‐hand side

Abstract and Applied Analysis, Volume 2004, Issue 6, Page 525-541, 2004., 2004
We investigate the existence of mild solutions on acompact interval to some classes of semilinear neutral functional differential inclusions. We will rely on a fixed‐point theorem for contraction multivalued maps due to Covitz and Nadler and on Schaefer′s fixed‐point theorem combined with lower semicontinuous multivalued operators with decomposable ...
M. Benchohra, E. Gatsori, S. K. Ntouyas
wiley   +1 more source

Existence and regularity of mild solutions in some interpolation spaces for functional partial differential equations with nonlocal initial conditions

Open Mathematics, 2018
This paper is devoted to study the existence and regularity of mild solutions in some interpolation spaces for a class of functional partial differential equations with nonlocal initial conditions. The linear part is assumed to be a sectorial operator in
Zhang Xuping, Chen Qiyu, Li Yongxiang
doaj   +1 more source

On a nonlinear compactness lemma in Lp(0, T; B)

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 27, Page 1725-1730, 2003., 2003
We consider a nonlinear counterpart of a compactness lemma of Simon (1987), which arises naturally in the study of doubly nonlinear equations of elliptic‐parabolic type. This paper was motivated by previous results of Simon (1987), recently sharpened by Amann (2000), in the linear setting, and by a nonlinear compactness argument of Alt and Luckhaus ...
Emmanuel Maitre
wiley   +1 more source

The Kneser property for abstract retarded functional differential equations with infinite delay

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 26, Page 1645-1661, 2003., 2003
We establish existence of mild solutions for a class of semilinear first‐order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.
Hernán R. Henríquez
wiley   +1 more source

Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

Mathematical Problems in Engineering, Volume 2003, Issue 2, Page 65-79, 2003., 2003
We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed‐point theorem. Examples are provided to illustrate the theory.
K. Balachandran, J. Y. Park
wiley   +1 more source