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Research Article | Open Access

A bounded resonant problem for the elliptic equation involving the square root of the Laplacian

Weijun Yan1,2, Zhiqi Xie2, Jiabao Su1( )
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
School of Mathematics and Statistics, Yulin University, Yulin 719000, China
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Abstract

In this paper, we obtained the existence of nontrivial solutions of the nonlocal elliptic equation involving the square root of the Laplacian with asymptotic linear resonance at infinity perturbed by a bounded nonlinearity. We made use of a penalized method, local linking and Morse theory.

Keywords

the square root of the Laplaciancritical groupsmorse theoryresonancelocal linking

References

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Electronic Research Archive
Volume 34 Issue 7,
July 2026
Pages 4947-4967
DOI: 10.3934/era.2026219

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Cite this article:
Yan W, Xie Z, Su J. A bounded resonant problem for the elliptic equation involving the square root of the Laplacian. Electronic Research Archive, 2026, 34(7): 4947-4967. https://doi.org/10.3934/era.2026219

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Received: 25 March 2026
Revised: 09 May 2026
Accepted: 28 May 2026
Published: 15 July 2026
©2026 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)