带小边值条件的半线性椭圆方程的可解性

摘要

In this paper, we prove the existence and non-existence of positive solutions of Semilinear equation with small Boundary value Conditions.By using of the Sub-super solution method and Schauder fixed point theorem , we prove the existence of the solutions.The existence and non-existence conditions of the solutions of the equation are obtained , and two examples to veri-fy the results are given.%利用上、下解方法及不动点等理论研究了带小边值条件的半线性 Laplace方程正解的存在性及不存在性，获得该类方程解的存在性条件和不存性条件，并给出实例验证了所得结果。