Existence of mild solutions of second-order neutral functional differential inclusions with nonlocal conditions in Banach spaces

S Marshal Anthoni,J.-H Kim,J P Dauer

doi:10.1155/s0161171204310410

Abstract

We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.

Highlights

In the two recent decades, existence problem for differential inclusions has attracted much attention
Differential inclusions represent an important generalization of differential equations
Ordinary and partial differential equations as modeling tools are too primitive to describe the behavior of many real dynamical systems

Summary

Introduction

In the two recent decades, existence problem for differential inclusions has attracted much attention. We prove the existence of mild solutions for second-order neutral functional differential and integrodifferential inclusions in Banach spaces.

Results

Conclusion