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.

Show me the PDF file (287 KB), TEX file, and other files for this article.

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

Return to the EJDE web page