Existence Of Positive Ground State Solutions For A Class Of Kirchhoff Type Equations

In this paper,we study the following nonlinear problem of Kirchoff type equation with pure power nonlinearities and two potentials:where e is a small positive parameter,a,b>0,2<p<6,V and W are two potentials.Under some proper assumptions,we obtain the existence of ground-state solutions of the above problem.Furthermore,we can extend the pure power nonlinearities |u|p-2u to the general nonlinearities f(u),we can also obtain the existence of ground-state solutions of the above problem.