The Existences Of The Solutions For A Class Of Nonlinear Elliptic Equations

In this paper,we study the existences of solutions for nonlinear elliptic equations,By making different hypotheses to the nonlinear term f（x,u）,we discuss respectively the existences of solutions for equations such as（?）and（?）In detail,this paper has been divided into the following three chapters:Chapter 1 We mainly introduce the writing background,and some preliminary knowledge which will be used in the process of the proofs.Chapter 2 In this chapter,by using local linking theorem,we discuss the exis-tences of solutions for the equation such as-?u+a（x）u=λf（x,u）.Chapter 3 In this chapter,by using mountain pass theorem,we discuss the exis-tences of solutions for the equation such as-?_pu+ξ|u|^p-2u=f（x,u）.