ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR NON-AUTONOMOUS SEMI-LINEAR SYSTEMS WITH NON-INSTANTANEOUS IMPULSES, DELAY, AND NON-LOCAL CONDITIONS

Abstract:

A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite dimensional Banach space. The existence and uniqueness of solutions on the interval [−r, τ] are obtained by applying Karakostas’ fixed-point theorem. Further results concerning solution prolongation are developed. An example is presented, and several remarks on the infinite-dimensional case are included.

Año de publicación:

2022

Keywords:

• Evolution equations
• DELAY
• Non-instantaneous impulses
• Karakostas’ fixed-point theorem
• Non-local conditions
• Non-autonomous systems

Fuente:

scopus

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