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

Weijun Yan; Zhiqi Xie; Jiabao Su; Weijun Yan; Zhiqi Xie; Jiabao Su

doi:10.3934/era.2026219

Electronic Research Archive

2026, Volume 34, Issue 7: 4947-4967. doi: 10.3934/era.2026219

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

1.
School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
2.
School of Mathematics and Statistics, Yulin University, Yulin 719000, China

Received: 25 March 2026 Revised: 09 May 2026 Accepted: 28 May 2026 Published: 09 June 2026

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.
- the square root of the Laplacian,
- critical groups,
- morse theory,
- resonance,
- local linking
Citation: Weijun Yan, Zhiqi Xie, Jiabao Su. A bounded resonant problem for the elliptic equation involving the square root of the Laplacian[J]. Electronic Research Archive, 2026, 34(7): 4947-4967. doi: 10.3934/era.2026219

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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.

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