Existence Results for Neutral and Second-Order Functional Differential Equations with Causal Operators in $L^p_{\mathrm{loc}}$ Spaces

Authors

  • Reemah Alhuzally Al-Baha University

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i1.7151

Keywords:

Neutral functional equations, casual operators, global existence, Volterra integral equations.

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.

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Published

2026-02-16

Issue

Vol. 19 No. 1: (January 2026)

Section

Differential Equations

License

Copyright (c) 2026 Reemah Alhuzally

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How to Cite

Existence Results for Neutral and Second-Order Functional Differential Equations with Causal Operators in $L^p_{\mathrm{loc}}$ Spaces. (2026). European Journal of Pure and Applied Mathematics, 19(1), 7151. https://doi.org/10.29020/nybg.ejpam.v19i1.7151