Demonstratio Mathematica (May 2025)

A generalized p-Laplacian problem with parameters

  • Zuo Jiabin,
  • Heidarkhani Shapour,
  • Moradi Shahin,
  • Sousa José Vanterler da Costa

DOI
https://doi.org/10.1515/dema-2025-0135
Journal volume & issue
Vol. 58, no. 1
pp. 623 – 636

Abstract

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In recent years, research into the multiplicity of solutions to the pp-Laplace operator problem has attracted attention, and several important results have been investigated and others still remain open. Problems involving a critical point are indeed interesting and relevant, especially challenging. Motivated by such questions, in this article, we are interested, through a critical point theorem, to investigate the existence of at least three distinct weak solutions for a generalized pp-Laplacian problem with parameters under appropriate hypotheses, applicable in physics, for instance, in fluid mechanics, and in Newtonian fluids. In this sense, as a direct consequence of the main result, we finish the work with two other results of weak solutions.

Keywords