A Critical Point Theorem for Perturbed Functionals and Low Perturbations of Differential and Nonlocal Systems-Reference-Cited by-同舟云学术

A Critical Point Theorem for Perturbed Functionals and Low Perturbations of Differential and Nonlocal Systems

Published:2020-06-11 Issue:3 Volume:20 Page:663-674
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bahrouni Anouar¹,Rădulescu Vicenţiu D.²^ORCID,Winkert Patrick³^ORCID

Affiliation:

1. Mathematics Department , Faculty of Sciences , University of Monastir , 5019 Monastir , Tunisia

2. Faculty of Applied Mathematics , AGH University of Science and Technology , 30-059 Kraków , Poland ; and Department of Mathematics, University of Craiova, 200585 Craiova, Romania; and Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

3. Institut für Mathematik , Technische Universität Berlin , Straße des 17. Juni 136, 10623 Berlin , Germany

Abstract

Abstract In this paper we establish a new critical point theorem for a class of perturbed differentiable functionals without satisfying the Palais–Smale condition. We prove the existence of at least one critical point to such functionals, provided that the perturbation is sufficiently small. The main abstract result of this paper is applied both to perturbed nonhomogeneous equations in Orlicz–Sobolev spaces and to nonlocal problems in fractional Sobolev spaces.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2020-2095/pdf

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