Geodesic
Remarks on least energy solutions for quasilinear elliptic problems in \(\mathbb R^N\)
Electronic journal of differential equations, Tome 2003 (2003)
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 
@article{EJDE_2003__2003__a159,
     author = {do \'O,  Jo\~ao Marcos and Medeiros,  Everaldo S.},
     title = {Remarks on least energy solutions for quasilinear elliptic problems in \(\mathbb {R^N\)}},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1109.35318},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a159/}
}
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JO  - Electronic journal of differential equations
PY  - 2003
VL  - 2003
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LA  - en
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%A Medeiros,  Everaldo S.
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%J Electronic journal of differential equations
%D 2003
%V 2003
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%G en
%F EJDE_2003__2003__a159
do Ó,  João Marcos; Medeiros,  Everaldo S. Remarks on least energy solutions for quasilinear elliptic problems in \(\mathbb R^N\). Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a159/