Existence of infinitely many radial solutions for quasilinear Schrodinger equations

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.

Keywords

• Quasilinear elliptic equations
• variational methods
• radial solutions