Results 21 to 30 of about 41 (41)
Abstract and Applied Analysis, Volume 2004, Issue 10, Page 881-896, 2004., 2004 Let u be a given bounded uniformly continuous mild solution of a higher‐order abstract functional differential equation of delay or advance type. We give a so‐called Massera‐type criterion for the existence of a mild solution, which is a “spectral component” of u with spectrum similar to the one of the forcing term f.
Nguyen Van Minh, Ha Binh Minh
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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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Linear neutral partial differential equations: a semigroup approach
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003 We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
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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
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Functional integro‐differential stochastic evolution equations in Hilbert space
International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 141-161, 2003., 2003 We investigate a class of abstract functional integro‐differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions.
David N. Keck, Mark A. McKibben
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Impulsive functional‐differential equations with nonlocal conditions
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 5, Page 251-256, 2002., 2002 The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional‐differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of a C0 semigroup of operators and the Banach contraction theorem are applied.
Haydar Akça +2 more
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International Journal of Stochastic Analysis, Volume 13, Issue 2, Page 171-179, 2000., 2000 Two theorems about the existence and uniqueness of mild and classical solutions of a semilinear functional‐differential evolution nonlocal Cauchy problem in a general Banach space are proved. Methods of semigroups and the Banach contraction theorem are applied.
Katarzyna Kolodziej
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International Journal of Stochastic Analysis, Volume 12, Issue 1, Page 91-97, 1999., 1998 The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional‐differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.
Ludwik Byszewski
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Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay
Nonautonomous Dynamical Systems, 2014 In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
Baliki Abdessalam, Benchohra Mouffak
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Semilinear Volterra integrodifferential equations with nonlocal initial conditions
Abstract and Applied Analysis, Volume 4, Issue 2, Page 127-139, 1999., 1999 We establish the global existence of mild solutions to a class of nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.
Sergiu Aizicovici, Mark Mckibben
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