Positive solution of quasilinear elliptic equations in RN with a bounded quasilinearity

Consider the quasilinear elliptic equation -div(A(u)∇ u) +1/2A'(u)|∇ u|²+V(x)u =(Iα |u|ᵖ) |u|ᵖ⁻²u in N,% where A∈ C¹(,) is a positive bounded function, V is a given potential and I_α denotes the Riesz potential with 0< α< N. While most existing works in the literature are concerned with the case where A is unbounded, little is known about the case where A is bounded. Under some general conditions on A and V, we establish the existence of a positive solution for the above equation by variational approach.