Accepted for publication in JNEEA

Existence Results for the Mild Solutions of Impulsive Semi-Linear Differential Equations

A. Chadha, D. N. Pandey

Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand, India

Received on January 20, 2015, revised version on September 27, 2018
Accepted on March 12, 2015

Communicated by Maximilian F. Hasler

Abstract.  In the present work, we consider a new class of impulsive semi-linear differential equations in arbitrary Banach space X with non-instantaneous impulses. We prove the existence of a mild solution to the impulsive differential equation with non-instantaneous impulses by virtue of the theory ofsemigroup via techniques of a new fixed point theorem for convex-power condensing operator.
Keywords: C0 semigroup, Convex-power condensing operator, Impulsive conditions, Measure of noncompactness.
2010 Mathematics Subject Classification:   34G10, 47D06.

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