奇异椭圆方程Robin问题多重正解的存在性

Existence of Multiple Positive Solutions for the Robin Problem of Singular Elliptic Equations

本文研究奇异椭圆方程Robin边值问题.首先运用Nehari流形方法解决带奇异项问题所对应泛函在零点处不可微的难点,其次应用Ekeland变分原理得到该问题对应泛函存在的临界点,最后通过极大值原理得到两个正解的存在性.

We consider the following the Robin boundary problem of singular elliptic equations.Firstly, Nehari manifold method is used to solve the difficulty that the functional with singular term cannot be differentiable at zero. Secondly, the critical points of the functional existence corresponding to this problem are obtained by using the Ekeland variational principle. Finally, the existence of two positive solutions is obtained by using the maximum principle.