Existence theorems for a nonlinear second-order distributional differential equation
Classical Analysis and ODEs
2018-10-03 v1
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.
Keywords
Cite
@article{arxiv.1704.08009,
title = {Existence theorems for a nonlinear second-order distributional differential equation},
author = {Wei Liu and Guoju Ye and Dafang Zhao and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1704.08009},
year = {2018}
}
Comments
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