On the solutions of the second-order $ (p, q) $-difference equation with an application to the fixed-point theory-Reference-Cited by-同舟云学术

On the solutions of the second-order $ (p, q) $-difference equation with an application to the fixed-point theory

Published:2024 Issue:5 Volume:9 Page:10679-10697
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Turan Nihan¹²,Başarır Metin¹,Şahin Aynur¹

Affiliation:

1. Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey

2. Department of Mathematics, Faculty of Arts and Sciences, İstanbul Beykent University, İstanbul 34500, Turkey

Abstract

<abstract><p>In this paper, we examined the existence and uniqueness of solutions to the second-order $ (p, q) $-difference equation with non-local boundary conditions by using the Banach fixed-point theorem. Moreover, we introduced a special case of this equation called the Euler-Cauchy-like $ (p, q) $-difference equation and provide its solution. We also studied the oscillation of solutions for this equation in $ (p, q) $-calculus and proved the $ (p, q) $-Sturm-type separation theorem and $ (p, q) $-Kneser theorem about the oscillation of solutions.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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