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Research Article | Open Access

Resonant problems for non-local elliptic operators with unbounded nonlinearites

Yutong Chen, Jiabao Su( )
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
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Abstract

In this paper we study the existence of nontrivial solutions of a class of asymptotically resonant problems driven by a non-local integro-differential operator with homogeneous Dirichlet boundary conditions by applying Morse theory and critical groups for a C 2 functional at both isolated critical points and infinity.

Keywords

integro-differential operatorvariational methodsresonancecritical groupMorse theory

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Electronic Research Archive
Volume 31 Issue 9,
September 2023
Pages 5716-5731
DOI: 10.3934/era.2023290

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Cite this article:
Chen Y, Su J. Resonant problems for non-local elliptic operators with unbounded nonlinearites. Electronic Research Archive, 2023, 31(9): 5716-5731. https://doi.org/10.3934/era.2023290

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Received: 11 April 2023
Revised: 28 June 2023
Accepted: 11 July 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)