带变号扰动的临界椭圆方程的两个正解的存在性

讨论了带变号扰动并且具有一定附加条件的临界椭圆方程的两个正解存在性.首先由变号扰动的正部对应的方程的正解和附加条件构造出原方程的一个上、下解，再由迭代方法和极值原理得到方程的第一个正解.考虑到方程的正解对参数没有单调性，因此，即使对于两个使得方程都有正解的参数，但在这两个参数之间的参数对应的方程不一定有正解.最后，如果方程存在第一个正解，那么由山路引理可得到方程的另一个正解.参7.

Existence of two positive solutions for critical elliptic equations with perturbation

This paper deals with the existence of two positive solutions for critical elliptic equations with a changed sign perturbation and with an auxiliary condition.First of all,the super-sub-solution can be obtained by this positive solution and by the auxiliary condition if perturbation is the positive side of the changed sign perturbation,and then the equation has a positive solution by the method of monotone in teraction and by the maximum principle.Because that the positive solution of the equation isn't monotone to parameter.Although all of the equations have a positive solution to two given parameters, the existence of the positive solutions of its equation to a parameter between the two given parameters can't be proved.Finally, if the first positive solution exits the second solution for the equation can be proved by the mountain pass lemma.7refs.