Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses

R. Poongodi 1 , V. T. Suveetha 2 and S. Dhanalakshmi 3

doi:10.26637/MJM0701/0006

Existence of mild solutions to partial neutral differential equations with non-instantaneous impulses

Authors :

R. Poongodi ¹ , V. T. Suveetha ² and S. Dhanalakshmi ³

Author Address :

¹ Research Scholar, Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu, India.
^{2, 3} Department of Mathematics, Kongunadu Arts and Science College, Coimbatore, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this article, we study the existence of $mathcal{PC}$-mild solutions for the initial value problems for a class of semilinear neutral equations. These equations have non-instantaneous impulses in Banach space and the corresponding solution semigroup is noncompact. We assume that the nonlinear terms satisfies certain local growth condition and a noncompactness measure condition. Also we assume the non-instantaneous impulsive functions satisfy some Lipschitz conditions.

Keywords :

Mild solutions, Non-instantaneous impulse, Noncompactness, Neutral systems.

DOI :

10.26637/MJM0701/0006

Article Info :

Received : July 21, 2018; Accepted : December 26, 2018.