The Solvability Of A Class Of Elliptic Problems Without AR Condition

In this paper, we consider the existence of weak solutions for the superlinear elliptic problems without AR condition. For example, let ?(?)Rn (n?3) is a bounded smooth domain, consider the following elliptic problemswhere p>1,? ?R1,?p = div((|?|p-2?)is the p-Laplace operator, and the non-cooperative elliptic systemH: ?×R2?R1 is a C1 function. AR condition guarantees the boundedness of the PS sequence of the functional I given by the corresponding problem. we can obtain the existence of the weak solution of the superlinear elliptic equation by using (PS)c form's Mountain pass lemma and obtain the existence of the weak solution of the superlinear el-liptic system by using (PS)c* form's Linking theorem in the case without the AR condition.