Geodesic
Remarks on least energy solutions for quasilinear elliptic problems in $\Bbb R^N$
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this work we establish some properties of the solutions to the quasilinear second-order problem $$ -\Delta_p w=g(w)\quad \hbox{in } \mathbb{R}^N $$ where $\Delta_p u=\mathop{\rm div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian operator and $ 1 lesss than p\leq N $. We study a mountain pass characterization of least energy solutions of this problem. Without assuming the monotonicity of the function $t^{1-p}g(t)$, we show that the Mountain-Pass value gives the least energy level. We also prove the exponential decay of the derivatives of the solutions.
Classification : 35J20, 35J60
Keywords: variational methods, minimax methods, superlinear elliptic problems, p-Laplacian, ground-states 
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     author = {do \'O, Jo\~ao Marcos and Medeiros, Everaldo S.},
     title = {Remarks on least energy solutions for quasilinear elliptic problems in $\Bbb R^N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a59/}
}
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do Ó, João Marcos; Medeiros, Everaldo S. Remarks on least energy solutions for quasilinear elliptic problems in $\Bbb R^N$. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a59/