9 resultados para differential equations
em Biblioteca Digital da Produção Intelectual da Universidade de São Paulo
Resumo:
In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.
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We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure functional differential equations. For both types of equations, we obtain results on the existence and uniqueness of solutions, continuous dependence, and periodic averaging.
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In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.
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We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.
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In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.
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In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.
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We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.
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In this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations. (C) 2012 Elsevier Inc. All rights reserved.
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In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.