Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 56, pp. 1-16.
Title: Existence of weak solutions for quasilinear elliptic equations
involving the p-Laplacian
Author: Uberlandio Severo (Univ. Federal da Paraiba, Brazil)
Abstract:
This paper shows the existence of nontrivial weak
solutions for the quasilinear elliptic equation
$$
-\big(\Delta_p u +\Delta_p (u^2)\big) +V(x)|u|^{p-2}u= h(u)
$$
in $\mathbb{R}^N$. Here $V$ is a positive continuous
potential bounded away from zero and $h(u)$ is a nonlinear term
of subcritical type.
Using minimax methods, we show the existence of a nontrivial solution
in $C^{1,\alpha}_{\rm loc}(\mathbb{R}^N)$ and then show that it
decays to zero at infinity when $1