含Caffarelli-Kohn-Nirenberg型临界指数奇异椭圆方程组的多重解

Multiple Solutions for Singular Elliptic Systems Involving Critical Exponents of Caffarelli-Kohn-Nirenberg Type

本文研究了有界域上一类含临界指数与奇异位势的非线性椭圆方程组,利用Caffarelli-Kohn-Nirenberg不等式与Nehari流形,证明了该类方程组在参数满足一定条件下两组非平凡解的存在性.

This paper deals with a class of nonlinear elliptic systems involves critical expo- nents and singular potentials in a bounded domain. By using the Caffarelli-Kohn-Nirenberg inequality and Nehari manifold, we prove that the system has least two nontrivial solutions when the pair of parameters （λ, δ） satisfies a certain conditions.