Abstract
This paper is concerned with the following quasilinear Schrödinger system in the entire space $\mathbb R^{N}$($N\geq3$): $$ \begin{cases} -\Delta u+A(x)u-\frac{1}{2} \triangle(u^{2})u=\frac{2\alpha}{\alpha+\beta} |u|^{\alpha-2}u|v|^{\beta},\\ -\Delta v+Bv-\frac{1}{2}\triangle(v^{2}) v=\frac{2\beta}{\alpha+\beta}|u|^{\alpha} |v|^{\beta-2}v. \end{cases} $$ By establishing a suitable constraint set and studying related minimization problem, we prove the existence of ground state solution for $\alpha,\beta > 1$, $2 < \alpha+\beta < \frac{4N}{N-2}$. Our results can be looked on as a generalization to results by Guo and Tang (Ground state solutions for quasilinear Schrödinger systems, J. Math. Anal. Appl. 389 (2012) 322).
Citation
Jianqing Chen. Qian Zhang. "Existence of ground state solution of Nehari-Pohožaev type for a quasilinear Schrödinger system." Differential Integral Equations 34 (1/2) 1 - 20, January/February 2021. https://doi.org/10.57262/die/1610420451
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