Geodesic
Multiple solutions for quasilinear elliptic equations with sign-changing potential
Electronic journal of differential equations, Tome 2016 (2016)
In this article, we study the quasilinear elliptic equation

$ -\Delta_{p} u-(\Delta_{p}u^{2})u+ V (x)|u|^{p-2}u=g(x,u), \quad x\in \mathbb{R}^N, $

where the potential $V(x)$ and the nonlinearity $g(x,u)$ are allowed to be sign-changing. Under some suitable assumptions on V and g, we obtain the multiplicity of solutions by using minimax methods.
Classification : 35B38, 35D05, 35J20
Keywords: quasilinear Schrödinger equation, symmetric mountain pass theorem, cerami condition 
@article{EJDE_2016__2016__a58,
     author = {Wang,  Ruimeng and Wang,  Kun and Teng,  Kaimin},
     title = {Multiple solutions for quasilinear elliptic equations with sign-changing potential},
     journal = {Electronic journal of differential equations},
     year = {2016},
     volume = {2016},
     zbl = {1334.35063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a58/}
}
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AU  - Wang,  Ruimeng
AU  - Wang,  Kun
AU  - Teng,  Kaimin
TI  - Multiple solutions for quasilinear elliptic equations with sign-changing potential
JO  - Electronic journal of differential equations
PY  - 2016
VL  - 2016
UR  - http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a58/
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%A Wang,  Ruimeng
%A Wang,  Kun
%A Teng,  Kaimin
%T Multiple solutions for quasilinear elliptic equations with sign-changing potential
%J Electronic journal of differential equations
%D 2016
%V 2016
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a58/
%G en
%F EJDE_2016__2016__a58
Wang,  Ruimeng; Wang,  Kun; Teng,  Kaimin. Multiple solutions for quasilinear elliptic equations with sign-changing potential. Electronic journal of differential equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a58/