带Dirichlet边界的椭圆方程组正解的存在性和不存在性

Existence and Nonexistence of Positive Solutions to Elliptic Equation System with Dirichlet Boundary Value

考察了一类带有Dirichlet边界条件的非线性椭圆型方程组的正解存在性和不存在性.主要运用了经典的特征值理论构造出方程的上下解,通过上下解方法证明了方程组正解的存在性和不存在性.

The paper investigates a nonlinear elliptic equation system with Dirichlet Boundary conditions,and constructs sub and super solution by the classical eigenvalue theory.Furthermore,the existence and nonexistence of positive solutions are proved through sub-super solution.