Existence theorems for a nonlinear second-order distributional differential equation

Abstract

In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are sharp.

This is a preprint of a paper whose final and definite form is with 'Journal of King Saud University - Science', ISSN 1018-3647. Submitted 05-March-2017; revised 24-April-2017; accepted for publication 26-April-2017