Geodesic
Existence of solutions to quasilinear Schrödinger equations with indefinite potential
Electronic journal of differential equations, Tome 2015 (2015)
In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation

$ -u''+V(x)u-(|u| ^2)''u=f(u) $

on $\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.
Classification : 37J45, 58E05, 34C37, 70H05
Keywords: quasilinear Schrödinger equation, local linking, Fountain theorem, indefinite potential 
@article{EJDE_2015__2015__a46,
     author = {Shen,  Zupei and Han,  Zhiqing},
     title = {Existence of solutions to quasilinear {Schr\"odinger} equations with indefinite potential},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1370.37118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a46/}
}
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AU  - Han,  Zhiqing
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VL  - 2015
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%A Han,  Zhiqing
%T Existence of solutions to quasilinear Schrödinger equations with indefinite potential
%J Electronic journal of differential equations
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%F EJDE_2015__2015__a46
Shen,  Zupei; Han,  Zhiqing. Existence of solutions to quasilinear Schrödinger equations with indefinite potential. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a46/