p-Laplace算子方程三点边值问题单调正解的存在性

Existence of Monotone Positive Solutions to a Type of Three-point Boundary Value Problem with p-Laplacian Operator

利用锥拉伸与锥压缩不动点定理,研究一类具p-Laplace算子的二阶微分方程的三点边值问题单调正解的存在性,给出了单调正解存在的充分条件,并确定了解曲线的凹凸性.

This paper deals with the existence of monotone positive solutions to a type of three point boundary value problems of nonlinear second-order differential equations with p-Laplacian operator. On the basis of the fixed point theorem on cone, sufficient conditions for the existence of monotone positive solutions are given to the boundary value problems with homogeneous and nonhomogeneous boundary conditions, respectively, and the convexity of solution curves is decided.