POSITIVE SOLUTIONS FOR ASYMPTOTICALLY PERIODIC KIRCHHOFF-TYPE EQUATIONS WITH CRITICAL GROWTH

In this paper‎, ‎we consider the following Kirchhoff-type equations‎:‎−‎(a+b∫R3|∇u|2)Δu+V(x)u=λ f(x,u)+u5‎,‎in R3, ‎u(x) 0‎,‎in R3,‎u∈H1(R3)‎,‎ ‎‎‎‎where a,b 0 are constants and λ is a positive parameter‎. ‎The aim of this paper is to study the existence of positive solutions for Kirchhoff-type equations with a nonlinearity in the critical growth under some suitable assumptions on V(x) and f(x,u)‎. ‎Recent results from the literature are improved and extended.