自然增长条件下含Hardy位势的椭圆型方程解的存在性

Existence of Solutions for Elliptic Equations Involving Hardy Potential under Natural Growth Condition

该文讨论自然增长条件下含Hardy位势的拟线性椭圆型方程解的存在性.我们把通常利用到的符号条件减弱到小于零的情况,证明此时方程对应的能量泛函仍满足(PS)条件,再利用不光滑泛函的临界点定理,证明方程存在着两个特性各异的非平凡解.

In this paper, the authors study a quasilinear elliptic equation with Hardy potential under natural growth condition. The authors extend the sign condition from nonnegative to a minus part, prove that at this time the corresponding functional of the equation still satisfies the （PS） condition, and then prove the existence of two nontrivial weak solutions via the nonsmooth critical point theory.