Existence Of Multiple Positive And Nodal Solutions Of Semilinear Elliptic Equations

In this paper,we consider the existence of the multiple positive and nodal so-lutions of a class of semilinear elliptic equations.When the nonlinear term f(x, u)=αg1(x,u)-γ|u|r-2u,we prove the existence of at least four solutions-two positive ,two negative,by using variational methods and the truncation technique. When the nonlinear term f(x,u)=αg1(x,u)+βg2(x,u)-γ|u|r-2u,we prove the existence of at least seven solutions-three positive,three negative,and one nodal solution-of the equation,by using variational methods, sub-and super-solution method,and the truncation technique.