### 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.

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.

#### Keywords

Quasilinear equation; variational methods; behaviour of solutions

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