On Existence Of Ground State Solution For A Class Of Quasilinear Elliptic Equation

In this thesis,we mainly probe into the following quasilinear elliptic equation:-?u+ V(x)u-k(?(1+u2)1/2)u/2(1+u2)1/2=h(u),x?R~N,where N?3,k>0,h:R?[0,+?)is a nonlinear function,V(x):R~N?R is a given positive potential,k>0.Under the assumption that the nonlinear term h(u)does't satisfy(AR)condition,the thesis proves that the equation has a ground state solution by using the variable substitution,the Mountain-Pass lemma and concentrated compact principle.The first section is devoted to introduce the background and the advance of previous researches on the equation and present the main result of the thesis.Section Two gives a preliminary analysis of the research results,which will be used in Section Three.