Abstract
AbstractIn 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.
Highlights
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
In this paper we are interested in the existence and attractivity of mild solutions of neutral state-dependent delay functional di erential equations
Using the xed point method combined with the semigroup theory in Fréchet space, Baghli and Benchohra [3,4,5] considered some classes of neutral evolution equations on unbounded intervals
Summary
We consider the existence and attractivity of mild solutions of the following neutral evolution equation with state- dependent delay. In this paper we are interested in the existence and attractivity of mild solutions of neutral state-dependent delay functional di erential equations. Su cient conditions are provided to get the global existence and attractivity of mild solutions of the problem (1) using Burton-Kirk’s xed point theorem (see [7]). The present paper provides su cient conditions for the existence and attractivity mild solutions to problem (1) in the Banach space setting. We assume that {A(t), t ≥ } is a family of closed densely de ned linear unbounded operators on the Banach space E and with domain D(A(t)) independent of t.
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