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

Uberlandio B. Severo, UFPB, Paraíba, Brazil

E. J. Qualitative Theory of Diff. Equ., No. 5. (2008), pp. 1-16.

Abstract: 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.

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