Geodesic
Existence of weak solutions for quasilinear elliptic equations involving the \(p\)-Laplacian
Electronic journal of differential equations, Tome 2008 (2008)
This paper shows the existence of nontrivial weak solutions for the quasilinear elliptic equation

$ -\big(\Delta_p u +\Delta_p (u^2)\big) +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 $C^{1,\alpha}_{\hbox{loc}}(\mathbb{R}^N)$ and then show that it decays to zero at infinity when $1$.
Classification : 35J20, 35J60, 35Q55
Keywords: quasilinear Schrödinger equation, solitary waves, p-Laplacian, variational method, mountain-pass theorem 
@article{EJDE_2008__2008__a34,
     author = {Severo,  Uberlandio},
     title = {Existence of weak solutions for quasilinear elliptic equations involving the {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1173.35483},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a34/}
}
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AU  - Severo,  Uberlandio
TI  - Existence of weak solutions for quasilinear elliptic equations involving the \(p\)-Laplacian
JO  - Electronic journal of differential equations
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VL  - 2008
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ID  - EJDE_2008__2008__a34
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%0 Journal Article
%A Severo,  Uberlandio
%T Existence of weak solutions for quasilinear elliptic equations involving the \(p\)-Laplacian
%J Electronic journal of differential equations
%D 2008
%V 2008
%U http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a34/
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%F EJDE_2008__2008__a34
Severo,  Uberlandio. Existence of weak solutions for quasilinear elliptic equations involving the \(p\)-Laplacian. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a34/