Infinitely many solutions for quasilinear Schrödinger equation with general superlinear nonlinearity

Abstract

Abstract In this article, we study the quasilinear Schrödinger equation − △ ( u ) + V ( x ) u − △ ( u 2 ) u = g ( x , u ) , x ∈ R N , $$ -\triangle (u)+V(x)u-\triangle \bigl(u^{2}\bigr)u=g(x,u), \quad x\in \mathbb{R}^{N}, $$ where the potential V ( x ) $V(x)$ and the primitive of g ( x , u ) $g(x,u)$ are allowed to be sign-changing. Under more general superlinear conditions on g, we obtain the existence of infinitely many nontrivial solutions by using the mountain pass theorem. Recent results in the literature are significantly improved.

Keywords

• Quasilinear Schrödinger equation
• Sign-changing potential
• Mountain pass theorem