Resonant problems for non-local elliptic operators with unbounded nonlinearites

Yutong Chen; Jiabao Su; Yutong Chen; Jiabao Su

doi:10.3934/era.2023290

Electronic Research Archive

2023, Volume 31, Issue 9: 5716-5731. doi: 10.3934/era.2023290

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Resonant problems for non-local elliptic operators with unbounded nonlinearites

Yutong Chen ,
Jiabao Su ^,

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received: 11 April 2023 Revised: 28 June 2023 Accepted: 11 July 2023 Published: 17 August 2023

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.
- integro-differential operator,
- variational methods,
- resonance,
- critical group,
- Morse theory
Citation: Yutong Chen, Jiabao Su. Resonant problems for non-local elliptic operators with unbounded nonlinearites[J]. Electronic Research Archive, 2023, 31(9): 5716-5731. doi: 10.3934/era.2023290

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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.

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