Multiplicity of solutions for a class of quasilinear elliptic equations with concave and convex terms in R
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)')...
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-02-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=295 |
| Summary: | 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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| ISSN: | 1417-3875 1417-3875 |