2024 A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators
Kanishka Perera, Caterina Sportelli
Topol. Methods Nonlinear Anal. 63(2): 717-731 (2024). DOI: 10.12775/TMNA.2023.037

Abstract

We study some critical elliptic problems involving the difference of two nonlocal operators, or the difference of a local operator and a nonlocal operator. The main result is the existence of two nontrivial weak solutions, one with negative energy and the other with positive energy, for all sufficiently small values of a parameter. The proof is based on an abstract result recently obtained in [22].

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Kanishka Perera. Caterina Sportelli. "A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators." Topol. Methods Nonlinear Anal. 63 (2) 717 - 731, 2024. https://doi.org/10.12775/TMNA.2023.037

Information

Published: 2024
First available in Project Euclid: 17 July 2024

Digital Object Identifier: 10.12775/TMNA.2023.037

Keywords: Critical elliptic problems , differences of local and nonlocal operators , multiplicity of solutions

Rights: Copyright © 2024 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.63 • No. 2 • 2024
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