Nonradial solutions for the critical quasi‐linear Hénon equation involving p‐Laplacian in RN

Abstract In this paper, we investigate the following ‐critical quasi‐linear Hénon equation involving ‐Laplacian where , , and . By carefully studying the linearized problem and applying the approximation method and bifurcation theory, we prove that, when the parameter takes the critical values for , the above quasi‐linear Hénon equation admits nonradial solutions such that and at . One should note that for when . Our results successfully extend the classical work of Gladiali, Grossi, and Neves concerning the Laplace operator (i.e., the case ) to the more general setting of the nonlinear ‐Laplace operator (). We overcome a series of crucial difficulties, including the nonlinear feature of the ‐Laplacian , the absence of Kelvin‐type transforms, and the lack of the Green integral representation formula.