一类含Hardy位势的超线性p-Laplace方程解的存在性

The Existence of Solutions for a Class of Super Linear p-Laplace Elliptic Equations Involving Hardy Potential

微分方程中的变分方法是将微分方程的求解问题转化为在一个恰当的Banach空间求相应泛函的临界点问题.为此,讨论了一类超线性p-Laplace方程,在假设方程不满足Ambrosetti-Rabinowitz(AR)条件的情况下,首先得到方程所对应泛函I的一个有界(PS)序列,进一步利用山路引理和(PS)条件,证明了该方程非平凡解的存在性.

Variational method of the differential equation is transformed into a question of finding the critical points of corresponding function in an appropriate Banach space.In this paper,we get a bounded（PS） sequence of the corresponding functional I,and the existence of trivial solutions for equation of superlinear p-Laplace elliptic equation without（AR） condition is studied with the help of using a variant version of the Mountain Pass Theorem and PS condition.