Existence and uniqueness of solution to nonlinear second-order distributional differential equations

Year 2020, Volume: 49 Issue: 1, 170 - 179, 06.02.2020

Feng Chen Guoju Ye Wei Liu Dafang Zhao

https://doi.org/10.15672/HJMS.2019.670

Abstract

The aim of this paper is to obtain solutions in terms of regulated functions to second-order distributional differential equations for Dirichlet problem. Existence and uniqueness theorems are established by using Schaefer's fixed point theorem and Banach's contraction mapping principle. Examples are given to demonstrate that the results are nontrivial.

Keywords

Regulated functions, Functions of bounded variation, Distributional differential equation, Schaefer’s fixed point theorem, Banach’s contraction mapping principle

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