Existence Results for Neutral and Second-Order Functional Differential Equations with Causal Operators in $L^p_{\mathrm{loc}}$ Spaces
Abstract
This paper studies the particular class of second order functional differential equations involving casual operators on a function space $L^p_{\mathrm{loc}}(\mathbb{R}_+, \mathbb{R}^n)$. Previous studies\cite{Corduneanu2008,Mahdavi2008} discussed this equations in the following different function spaces$C(\mathbb{R}_+,\mathbb{R}^n)$ and $L^2_{\mathrm{loc}}(\mathbb{R}_+,\mathbb{R}^n)$. We establish the existence and uniqueness of solutions for both linear and nonlinear cases. Our worked based on the resolvent kernel method, Hölder's inequality, and successive approximation techniques. Finally, We provide examples to illustrate our results.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Differential Equations and Boundary Problems
Fuzzy Systems and Optimization
Publication details
- Journal / source
- European Journal of Pure and Applied Mathematics
- Volume
- 19
- Issue
- 1
- Pages
- 7151–7151
- Publication date
- 16 February 2026
- Language
- EN