Existence and concentration of nodal solutions to a class of quasilinear problems

Abstract

The existence and concentration behavior of nodal solutions are established for the equation $-\varepsilon^{p} \Delta_{p}u + V(z)|u|^{p-2}u=f(u)$ in $\Omega$, where $\Omega$ is a domain in ${\mathbb R}^{N}$, not necessarily bounded, $V$ is a positive Hölder continuous function and $f\in C^{1}$ is a function having subcritical growth.