Existence of positive solutions for a class of quasilinear Schrِdinger equations on

In this paper, we study the following quasilinear Schrödinger equation of the form − △ u + V ( x ) u − 1 2 △ ( u 2 ) u = α | u | p − 1 u + β | u | q − 1 u , x ∈ R N , where N ≥ 3 , 2 + 2 N ≤ q < p < 2 ⋅ ( 2 N N − 2 ) − 1 , α , β ∈ R N . Under appropriate assumptions on V ( x ) , we establish the existence of ground state solutions by a minimization argument.