A generalized <i>p</i> -Laplacian problem with parameters

Abstract In recent years, research into the multiplicity of solutions to the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -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.