Existence of a bound state solution for quasilinear Schrödinger equations

Abstract

In this article, we establish the existence of bound state solutions for a class of quasilinear Schrödinger equations whose nonlinear term is asymptotically linear in ℝN{\mathbb{R}^{N}}. After changing the variables, the quasilinear equation becomes a semilinear equation, whose respective associated functional is well defined in H1⁢(ℝN){H^{1}(\mathbb{R}^{N})}. The proofs are based on the Pohozaev manifold and a linking theorem.

Keywords

• quasilinear schrödinger equation
• asymptotically linear
• barycenter
• linking
• pohozaev manifold
• 35j62
• 35j20
• 35b09