Existence of ground state solutions for quasilinear Schrödinger equations with general Choquard type nonlinearity

Abstract

Abstract In this paper, we study the following Choquard type quasilinear Schrödinger equation: − Δ u + u − Δ ( u 2 ) u = ( I α ∗ G ( u ) ) g ( u ) , x ∈ R N , $$ -\Delta u+u-\Delta \bigl(u^{2}\bigr)u=\bigl(I_{\alpha }*G(u) \bigr)g(u),\quad x\in {\mathbb{R}}^{N}, $$ where N ≥ 3 $N\geq 3$ , 0 < α < N $0<\alpha <N$ , and I α $I_{\alpha }$ is a Riesz potential. By using the minimization method developed by (Tang and Chen in Adv. Nonlinear Anal. 9:413–437, 2020; Willem in Minimax Theorems, 1996), we establish the existence of ground state solutions with general Choquard type nonlinearity. Our results extend the results obtained by (Chen et al. in Appl. Math. Lett. 102:106141, 2020).

Keywords

• Quasilinear Schrödinger equation
• Ground state solutions
• Pohozaev identity
• General Choquard type nonlinearity