Results 21 to 30 of about 60 (60)
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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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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Advances in Nonlinear Analysis, 2014 In this article we study the existence of positive periodic solutions for a fourth-order nonlinear neutral differential equation with variable delay.
Ardjouni Abdelouaheb +2 more
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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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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces.
Mallika D. +3 more
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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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International Journal of Differential Equations, Volume 2024, Issue 1, 2024.This paper investigates the existence and controllability of second‐order functional differential equations with infinite delay, incorporating random operators. The existence of solutions is established using the Schauder fixed point theorem, ensuring that solutions exist under specified conditions.
Srinivasan Madhumitha +5 more
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Almost periodic mild solutions of a class of partial functional differential equations
Abstract and Applied Analysis, Volume 3, Issue 3-4, Page 425-436, 1998., 1998 We study the existence of almost periodic mild solutions of a class of partial functional differential equations via semilinear almost periodic abstract functional differential equations of the form To this end, we first associate with every almost periodic semilinear equation a nonlinear semigroup in the space of almost periodic functions.
Bernd Aulbach, Nguyen Van Minh
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