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In this paper, we study the following generalized quasilinear Schrödinger equation: $$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u),\,\, x\in {\mathbb {R}}^N, \end{aligned}$$-div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN, where $$N\ge 3$$N≥3, $$2^*=\frac{2N}{N-2}$$2∗=2NN-2, $$g\in \mathcal {C}^1({\mathbb {R}},{\mathbb {R}}^{+})$$g∈C1(R,R+), V(x)… Click to show full abstract
In this paper, we study the following generalized quasilinear Schrödinger equation: $$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u),\,\, x\in {\mathbb {R}}^N, \end{aligned}$$-div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u=f(x,u),x∈RN, where $$N\ge 3$$N≥3, $$2^*=\frac{2N}{N-2}$$2∗=2NN-2, $$g\in \mathcal {C}^1({\mathbb {R}},{\mathbb {R}}^{+})$$g∈C1(R,R+), V(x) is 1-periodic or a bounded potential well. Using a change of variable, we obtain the existence of ground states for this problem using the Mountain Pass Theorem. Our results generalize some existing results.
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
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