Positive solutions for a class of generalized quasilinear Schrödinger equation involving concave and convex nonlinearities in Orilicz space

In this paper, we study the following generalized quasilinearSchrödinger equation − div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = λ f ( x , u ) + h ( x , u ) , x ∈ R N , where λ > 0 , N ≥ 3 , g ∈ C 1 ( R , R + ) . By using a change ofvariable, we obtain the existence of positive solutions for this problemwith concave and convex nonlinearities via the Mountain Pass Theorem. Ourresults generalize some existing results.