Geodesic
Multiple solutions for quasilinear elliptic equations with sign-changing potential
Electronic Journal of Differential Equations, Tome 2016 (2016).

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Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a25/}
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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__a25/