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

Authors
  • Bahrouni, Anouar1
  • Rădulescu, Vicenţiu D.2
  • Winkert, Patrick3
  • 1 University of Monastir, Faculty of Sciences, 5019 , (Tunisia)
  • 2 AGH University of Science and Technology, 30-059, 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 , (Poland)
  • 3 Technische Universität Berlin, Straße des 17. Juni 136, 10623 , (Germany)
Type
Published Article
Journal
Advanced Nonlinear Studies
Publisher
De Gruyter
Publication Date
Jun 11, 2020
Volume
20
Issue
3
Pages
663–674
Identifiers
DOI: 10.1515/ans-2020-2095
Source
De Gruyter
Keywords
License
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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.

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