Abstract
Using the Kuratowski measure of noncompactness and progressive estimation method, we obtain the existence results of mild solutions for impulsive partial neutral second-order functional integro-differential equations with infinite delay in Banach spaces. The compactness condition of the impulsive term, some restrictive conditions on ap rioriestimation and noncompactness measure estimation have been deleted. Our conditions are simple and our results essentially improve and extend some known results. As applications, some examples are provided to illustrate the obtained results. MSC: 34K30; 34K40; 35R10; 47D09
Highlights
Consider the following impulsive partial neutral second-order functional integro-differential systems with infinite delay in a Banach space X: ⎧ ⎪⎪⎪⎪⎪⎨d dt [x (t) + g (t, t ∈ [, b], xt, t k (t, s, xs) ds)] = Ax(t) + g (t, xt k (t, s, xs) ds), ⎪⎪⎪⎪⎪⎩x x=(tφi)
Impulsive partial neutral functional differential equations 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 [ – ], authors used a strict set contraction mapping fixed point theorem without the compactness assumption on the associated family of operators to obtain the existence results of system ( ) when gi(t, xt) is not an integral operator and the following system:
Summary
Consider the following impulsive partial neutral second-order functional integro-differential systems with infinite delay in a Banach space X:. N, where A is the infinitesimal generator of a strongly continuous cosine function of bounded linear operators, (C(t))t∈R, on X. Impulsive partial neutral functional differential equations 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. With regard to this matter, we refer the reader to [ – ] and references therein.
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