Existence of weak solutions for quasilinear elliptic equations involving the p-Laplacian
This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation $$ -ig(Delta_p u +Delta_p (u^2)ig) +V(x)|u|^{p-2}u= h(u) $$ 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...
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Veröffentlicht in: | Electronic journal of differential equations 2008-04, Vol.2008 (56), p.1-16 |
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Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation $$ -ig(Delta_p u +Delta_p (u^2)ig) +V(x)|u|^{p-2}u= h(u) $$ 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 $C^{1,alpha}_{ m loc}(mathbb{R}^N)$ and then show that it decays to zero at infinity when $1 |
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ISSN: | 1072-6691 |