Electron. J. Diff. Equ., Vol. 2014 (2014), No. 230, pp. 1-18.

Existence of infinitely many radial solutions for quasilinear Schrodinger equations

Gui Bao, Zhi-Qing Han

Abstract:
In this article we prove the existence of radial solutions with arbitrarily many sign changes for quasilinear Schrodinger equation
$$ -\sum_{i,j=1}^{N}\partial_j(a_{ij}(u)\partial_iu) +\frac{1}{2}\sum_{i,j=1}^{N}a'_{ij}(u)\partial_iu\partial_ju+V(x)u =|u|^{p-1}u,~x\in\mathbb{R}^N, $$
where $N\geq3$, $p\in(1,\frac{3N+2}{N-2})$. The proof is accomplished by using minimization under a constraint.

Submitted September 1, 2014. Published October 27, 2014.
Math Subject Classifications: 37J45, 58E05, 34C37,70H05.
Key Words: Quasilinear elliptic equations; variational methods; radial solutions.

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Gui Bao
School of Mathematics and Statistics Science
Ludong University
Yantai, Shandong 264025, China
email: baoguigui@163.com
Zhiqing Han
School of Mathematical Sciences
Dalian University of Technology
Dalian 116024, China
email: hanzhiq@dlut.edu.cn

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