Multiple Solutions For A Class Of Semilinear Elliptic Equations

In this paper,We study the following a class of semilinear elliptic equations-?u+a(x)u=g(x,u),x??,u=0,x?(?)?.By using variational methods and critical point theorem,we establish three criterions to guarantee that the above system has infinitely many notrivial solutions under the assumption that gis asymptotically linear and superlinear.Recent results in the literature are improved and generalized.This article is divided into three chapters.In Chapter 1,the background and significance,status at home and abroad,main works of this dissertation are introduced.In Chapter 2,on the assumption that the nonlinearity g satisfies a weaker asymptotical condition,we use mountain pass lemma to prove that the equation has infinitely many nontrivial solutions.In Chapter 3,On the assumption that the nonlinearity g satisfies the more general local supquadratic condition,we choose a bounded open area.it is proved by fountain theorem that the above equation has infinitely many nontrivial solutions.