Existence Of Solutions For A Class Of Elliptic Partial Differential Equations With ?_? Operators

In this article,the existence,multiplicity non-trivial ground state solutions of the following elliptical partial differential equation solutions with degenerative operators ??are mainly studied.Firstly,we study the following semi-linear degenerate Schrodinger equation:where 10,the nonlinear term f(x,u)satisfies super-linear or sub-linear condition at infinity,we obtain the non-trivial ground state solution of the equation by using the mountain pass theorem and the Ekeland variational principle.When V(x)is sign changing potential,the nonlinear termf(x,u)satisfies super-linear condition at infinity and the linking theorem is used to obtain a non-trivial solution to the equation.