Existence of Solutions for a Class of Volterra Integral Equations on Time Scales

被引：0

作者：

Ramadan, Wafaa Salih ^{[1
]}

Georgiev, Svetlin G. ^{[2
]}

Al-Hayani, Waleed ^{[3
]}

机构：

[1] Univ Al Hamdaniya, Coll Educ Pure Sci, Dept Math, Ninevah, Iraq

[2] Sorbonne Univ, Dept Math, Paris, France

[3] Univ Mosul, Coll Comp Sci & Math, Dept Math, Mosul, Iraq

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2025年 / 48卷 / 06期

关键词：

fixed point; global solutions; sum of operators; Volterra integral equation;

D O I：

10.1002/mma.10702

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a class of Volterra integral equations for existence of global classical solutions. We give conditions under which the considered equations have at least one and at least two classical solutions. To prove our main results, we propose a new approach based upon recent theoretical results. More precisely, we give a suitable integral representation of the solutions of the considered Volterra integral equation. Then, we construct two operators for which any fixed point of their sum is a solution of the considered Volterra integral equation.

引用

页码：6647 / 6653

页数：7

共 10 条

[1]

Agarwal RaviP., 2001, CAMB TRACT MATH

[2] FIXED POINT INDEX THEORY FOR PERTURBATION OF EXPANSIVE MAPPINGS BY k-SET CONTRACTIONS [J].

Djebali, Smail ;

Mebarki, Karima .

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 54 (02) :613-640

[3]

Drabek P., 2007, Methods of Nonlinear Analysis - Applications to Differential Equations

[4]

Georgiev S., Palestine Journal of Mathematics

[5]

Mebarki K., 2023, Fixed Point Theorems with Applications

[6] EXISTENCE OF SOLUTIONS FOR A CLASS OF FIRST ORDER BOUNDARY VALUE PROBLEMS [J].

Mouhous, Amirouche ;

Georgiev, Svetlin Georgiev ;

Mebarki, Karima .

ARCHIVUM MATHEMATICUM, 2022, 58 (03) :141-158

[7] A nonstandard Volterra integral equation on time scales [J].

Reinfelds, Andrejs ;

Christian, Shraddha .

DEMONSTRATIO MATHEMATICA, 2019, 52 (01) :503-510

[8] A high accurate and convergent numerical framework for solving high-order nonlinear Volterra integro-differential equations [J].

Yang, Yin ;

Tohidi, Emran ;

Deng, Guoting .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2023, 421

[9] High accurate convergent spectral Galerkin methods for nonlinear weakly singular Volterra integro-differential equations [J].

Yang, Yin ;

Deng, Guoting ;

Tohidi, Emran .

COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (04)

[10] Rigorous convergence analysis of Jacobi spectral Galerkin methods for Volterra integral equations with noncompact kernels [J].

Yang, Yin ;

Tohidi, Emran ;

Ma, Xiaohua ;

Kang, Sujuan .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 366

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