Abstract
In this article, we study the existence of mild solutions for a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and non-instantaneous impulses in separable Hilbert spaces. The new results are obtained by using the Hausdorff measure of noncompactness, and the theory of analytic resolvent operators and fractional power of closed operators with the fixed point theorems. An example is also given to illustrate the obtained theory.
Highlights
The study of impulsive functional differential and integro-differential systems is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution
Impulsive partial neutral functional differential and integro-differential systems have become an important object of investigation in recent years stimulated by their numerous applications to problems arising in mechanics, electrical engineering, medicine, biology, ecology, etc
In this paper we consider the existence of a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and non-instantaneous impulses of the form in Hilbert spaces of the form t d x(t) – G(t, xt) = A x(t) + h(t – s)x(s) ds dt + f (t, xt) dt + F(t, xt) dw(t)
Summary
The study of impulsive functional differential and integro-differential systems is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution. Lin et al [ ] discussed the existence of mild solutions for a class of neutral impulsive stochastic integro-differential equations with infinite delays and analytic resolvent operators. Pierri et al [ ] studied the existence of solutions for a class of first order semilinear abstract impulsive differential equations with non-instantaneous impulses by using the theory of analytic semigroup and fractional power of closed operators. Yan and Lu [ ] discussed a class of fractional impulsive partial stochastic integro-differential equations with non-instantaneous impulses in Hilbert spaces under the Lipschitz conditions. In this paper we consider the existence of a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and non-instantaneous impulses of the form in Hilbert spaces of the. Lemma . (Darbo-Sadovskii [ ]) If W ⊆ Y is bounded closed and convex, the continuous map : W → W is a χY -contraction, the map has at least one fixed point in W
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