Results 21 to 30 of about 437 (100)
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
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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
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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
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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
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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
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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
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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
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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
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International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 163-170, 2003., 2003 The existence of mild solutions of Sobolev‐type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.
M. Kanakaraj, K. Balachandran
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Integrodifferential equations with analytic semigroups
International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 177-189, 2003., 2003 In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.
D. Bahuguna
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