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In this paper, we study the following quasilinear Schrödinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$-Δu+V(x)u-Δ(u2)u=g(x,u),x∈RNwhere V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$x1,…,xN,… Click to show full abstract
In this paper, we study the following quasilinear Schrödinger equation of the form $$\begin{aligned} -\Delta u+V(x)u-\Delta (u^{2})u= g(x,u),~~~ x\in \mathbb {R}^N \end{aligned}$$-Δu+V(x)u-Δ(u2)u=g(x,u),x∈RNwhere V and g are 1-periodic in $$x_{1},\ldots ,x_{N}$$x1,…,xN, and g is a superlinear but subcritical growth as $$|u|\rightarrow \infty $$|u|→∞. We develop a more direct and simpler approach to prove the existence of ground state solutions.
Keywords:
dinger equation;
state solutions;
quasilinear schr;
ground state;
schr dinger
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
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Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
Link to full text (if available)
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recommendations!