A generalized p-Laplacian problem with parameters

Abstract

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

• three solutions
• p-laplacian type
• critical point
• variational methods
• 35j25
• 35j62