Research article

On multiple solutions for an elliptic problem involving Leray–Lions operator, Hardy potential and indefinite weight with mixed boundary conditions

  • Received: 20 January 2025 Revised: 03 March 2025 Accepted: 05 March 2025 Published: 11 March 2025
  • MSC : 35J15, 35J20, 35J25

  • This paper concentrates on establishing the existence of multiple weak solutions for a specific type of elliptic equations that involve a Hardy potential and have mixed boundary conditions. The main goal of the study is to establish an existence result of at least three different weak solutions thanks to variational techniques, Hardy inequality, and a particular theorem called the Bonanno–Marano type three critical points theorem.

    Citation: Khaled Kefi, Mohammed M. Al-Shomrani. On multiple solutions for an elliptic problem involving Leray–Lions operator, Hardy potential and indefinite weight with mixed boundary conditions[J]. AIMS Mathematics, 2025, 10(3): 5444-5455. doi: 10.3934/math.2025251

    Related Papers:

  • This paper concentrates on establishing the existence of multiple weak solutions for a specific type of elliptic equations that involve a Hardy potential and have mixed boundary conditions. The main goal of the study is to establish an existence result of at least three different weak solutions thanks to variational techniques, Hardy inequality, and a particular theorem called the Bonanno–Marano type three critical points theorem.



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    [2] G. Bonanno, S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 89 (2010), 1–10. https://doi.org/10.1080/00036810903397438 doi: 10.1080/00036810903397438
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