Multiplicity of solutions for a class of quasilinear elliptic equations with concave and convex terms in R

• Main Author: Uberlandio Severo
• Format: Article
• Language: English
• Published: University of Szeged 2008-02-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=295

In this paper the Fountain theorem is employed to establish infinitely many solutions for the class of quasilinear Schr\"{o}dinger equations $-L_pu+ V(x)|u|^{p-2}u=\lambda|u|^{q-2}u+\mu |u|^{r-2}u$ in $\mathbb{R}$, where $L_pu=(|u'|^{p-2}u')'+ (|(u^2)'|^{p-2}(u^2)')'u$, $\lambda, \mu$ are real parameters, $1 < p < \infty$, $1<q<p$, $r>2p$ and the potential $V(x)$ is nonnegative and satisfies a suitable integrability condition.