Electron. J. Differential Equations, Vol. 2017 (2017), No. 114, pp. 1-15.

Ground state solutions for a quasilinear Schrodinger equation with singular coefficients

Jixiu Wang, Qi Gao, Li Wang

Abstract:
In this article, we study the quasilinear Schrodinger equation with the critical exponent and singular coefficients,
$$ -\Delta u +V(x)u-\Delta(|u|^2)u=\lambda\frac{|u|^{q-2}u}{|x|^{\mu}} +\frac{|u|^{22^*(\nu)-2}u}{|x|^\nu}\quad\text{in } \mathbb{R}^N, $$
where $N\geq 3$, $2<q<22^*(\mu)$, $2^*(s)=\frac{2(N-s)}{N-2}$, and $\lambda, \mu, \nu$ are parameters with $\lambda>0$, $\mu, \nu \in [0,2)$. By applying the Mountain Pass Theorem and the Concentration Compactness Principle, we establish the existence of the ground state solutions to the above problem.

Submitted March 7, 2017. Published April 27, 2017.
Math Subject Classifications: 35J62, 35J60, 35J20.
Key Words: Quasilinear Schrodinger equations; critical exponent; ground state solutions; calculus of variations.

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Jixiu Wang
School of Mathematics and Computer Science
Hubei University of Arts and Science
Xiangyang 441053, China
email: wangjixiu127@163.com
Qi Gao
Department of Mathematics
School of Science
Wuhan University of Technology
Wuhan 430070, China
email: gaoq@whut.edu.cn
Li Wang
College of Science
East China Jiaotong University
Nanchang 330013, China
email: wangli.423@163.com

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