Nodal solutions for a generalized quasilinear Schrödinger equation with critical exponents

Abstract

This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrodinger equations in \begin{document} $\mathbb{R}^N$ \end{document} with critical growth which arise from plasma physics, fluid mechanics, as well as the self-channeling of a high-power ultashort laser in matter. We find the critical exponents for a generalized quasilinear Schrodinger equations and obtain the existence of sign-changing solution with k nodes for any given integer \begin{document} $k ≥ 0$ \end{document} .