Elsevier

Applied Mathematics Letters

Volume 24, Issue 11, November 2011, Pages 1810-1816
Applied Mathematics Letters

Existence results for some partial functional differential equations with state-dependent delay

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Abstract

In this paper, we establish sufficient conditions for the existence of solutions for some partial functional differential equations with state-dependent delay; we assume that the linear part is not necessarily densely defined and satisfies the well-known Hille–Yosida conditions. Our approach is based on a nonlinear alternative of Leray–Schauder type and integrated semigroup theory. An application is provided to a reaction–diffusion equation with state-dependent delay.

Keywords

Nondensely defined operator
Partial functional differential equation
State-dependent delay
Fixed point
Integrated semigroups
Integral solutions

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