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

Objective & Hypothesis:The aim of this paper is to obtain solutions in terms of regulated functions to second-order distributional differential equations for Dirichlet problem.

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Key Findings & Data:Existence and uniqueness theorems are established by using Schaefer's fixed point theorem and Banach's contraction mapping principle.

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Conclusion & Impact:Examples are given to demonstrate that the results are nontrivial.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Regulated functions · Functions of bounded variation · Distributional differential equation

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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Cite This Article

Chen, F., Ye, G., Liu, W., Zhao, D. (2020). Existence and uniqueness of solution to nonlinear second-order distributional differential equations. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/HJMS.2019.670

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