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Ground States for a Class of Generalized Quasilinear Schrödinger Equations in \({\mathbb {R}}^N\)

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Abstract

In this paper, we study the following generalized quasilinear Schrödinger equation:

$$\begin{aligned} -\text {div}(g^2(u)\nabla u)+g(u)g'(u)|\nabla u|^2+V(x)u=f(x,u),\,\, x\in {\mathbb {R}}^N, \end{aligned}$$

where \(N\ge 3\), \(2^*=\frac{2N}{N-2}\), \(g\in \mathcal {C}^1({\mathbb {R}},{\mathbb {R}}^{+})\), 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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Jianhua Chen & Xianhua Tang

  2. School of Mathematics and Statistics, Qujing Normal University, Qujing, 655011, Yunnan, People’s Republic of China

    Bitao Cheng

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  1. Jianhua Chen
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  2. Xianhua Tang
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  3. Bitao Cheng
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Correspondence to Xianhua Tang.

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Chen, J., Tang, X. & Cheng, B. Ground States for a Class of Generalized Quasilinear Schrödinger Equations in \({\mathbb {R}}^N\) . Mediterr. J. Math. 14, 190 (2017). https://doi.org/10.1007/s00009-017-0990-y

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  • DOI: https://doi.org/10.1007/s00009-017-0990-y

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