New Results On the asymptotic behavior of solutions of $N$-th order forced integro-differential equations with $\beta$-Laplacian-Reference-Cited by-同舟云学术

New Results On the asymptotic behavior of solutions of $N$-th order forced integro-differential equations with $\beta$-Laplacian

Published:2022-12-31 Issue: Volume: Page:1-8
ISSN:2651-477X
Container-title:Hacettepe Journal of Mathematics and Statistics
language:en
Short-container-title:

Author:

GRACE Said R.¹^ORCID,GRAEF John R.²,TUNÇ Ercan³

Affiliation:

1. Cairo University

2. University of Tennessee at Chattanooga

3. Tokat Gaziosmanpasa University

Abstract

The authors prove some new results on the asymptotic behavior of solutions of $n$th order forced integro-differential equations with a $\beta$-Laplacian. The main goal is to investigate when all solutions behave at infinity like certain nontrivial nonlinear functions. They apply a technique involving Young's inequality. The paper concludes with two examples illustrating the applicability of the main results.

Publisher

Hacettepe University

Subject

Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis

Reference18 articles.

1. Reference 1 M. Bohner, S. R. Grace, N. Sultana, \emph{Asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations}, Opuscula Math. \textbf{34} (2014), 5--14.

2. Reference 2 E. Brestovansk\'{a}, M. Medve\v{d}, \emph{Asymptotic behavior of solutions to second-order differential equations with fractional derivative perturbations}, Electron. J. Differ. Eq. \textbf{2014} (2014), No. 201, 1--10.

3. Reference 3 B. C. Dhage, A. V. Deshmukh, J. R. Graef, {\it On asymptotic behavior of a nonlinear functional integral equation}, Commun. Appl. Nonlinear Anal. {\bf 15} (2008), 55--67.

4. Reference 4 S. R. Grace, J. R. Graef, S. Panigrahi, E. Tun\c{c}, \emph{On the oscillatory behavior of Volterra integral equations on time-scales}, PanAmerican Math. J. \textbf{23} (2013), 35--41.

5. Reference 5 S. R. Grace, J. R. Graef, E. Tun\c{c}, \emph{On the asymptotic behavior of solutions of certain integro-differential equations}, J. Appl. Anal. Computation {\bf 9} (2019), 1305--1318.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A New Nonlinear Integral Inequality with a Tempered Ψ–Hilfer Fractional Integral and Its Application to a Class of Tempered Ψ–Caputo Fractional Differential Equations;Axioms;2024-05-01