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

Claudianor O. Alves, Giovany M. Figueiredo

DOI: http://dx.doi.org/10.12775/TMNA.2007.012

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.

Keywords


Quasilinear equation; variational methods; behaviour of solutions

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