Opuscula Math. 45, no. 5 (2025), 623-645
https://doi.org/10.7494/OpMath.2025.45.5.623

 
Opuscula Mathematica

Nontrivial solutions for Neumann fractional p-Laplacian problems

Chun Li
Dimitri Mugnai
Tai-Jin Zhao

Abstract. In this paper, we investigate some classes of Neumann fractional \(p\)-Laplacian problems. We prove the existence and multiplicity of nontrivial solutions for several different nonlinearities, by using variational methods and critical point theory based on cohomological linking.

Keywords: fractional \(p\)-Laplacian, Neumann boundary condition, linking over cones.

Mathematics Subject Classification: 35A15, 47J30, 35S15, 47G10, 45G05.

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  • Chun Li
  • Southwest University, School of Mathematics and Statistics, Chongqing 400715, P.R. China
  • Tai-Jin Zhao
  • Southwest University, School of Mathematics and Statistics, Chongqing 400715, P.R. China
  • Communicated by Vicenţiu D. Rădulescu.
  • Received: 2025-08-08.
  • Revised: 2025-09-02.
  • Accepted: 2025-09-02.
  • Published online: 2025-09-13.
Opuscula Mathematica - cover

Cite this article as:
Chun Li, Dimitri Mugnai, Tai-Jin Zhao, Nontrivial solutions for Neumann fractional p-Laplacian problems, Opuscula Math. 45, no. 5 (2025), 623-645, https://doi.org/10.7494/OpMath.2025.45.5.623

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