一类半线性椭圆型方程组正解的存在性

摘要

主要研究一类半线性椭圆型方程组正解的存在性.利用变分法将椭圆型方程组解的问题转化为相应能量泛函的临界点问题, 进一步证明了方程组能量泛函临界点的存在性.%This paper mainly studies the existence of positive solutions for a class of semilinear elliptic systems. By using the variational method, the problem of solving elliptic equations is transformed into the critical point problem of the corresponding energy functional, and the existence of the critical point of the energy functional of the equations is further proved.