三阶p-Laplacian边值问题解的存在唯一性定理

Existence and Uniqueness of Solution to Third-Order Boundary Value Problem with p-Laplacian Operator

利用不动点定理和积分方程来研究含有p-Laplacian算子的三阶三点非线性边值问题解的存在唯一性边界值问题.将方程解的存在唯一性问题等价转换为一个积分算子不动点的存在唯一性,然后利用Banach不动点定理给出了此边值问题解的存在唯一性的充分条件,对现有的相关结果作了进一步推广,同时为含有p-Laplacian算子的边值问题的研究奠定了一定的理论基础.

Using the fixed point theorem and the integral equation, we established the sufficient condition of the existence and uniqueness of solution to the nonlinear third-order three-point boundary value problem with p-Laplacian operator. The problem was equivalent to the existence and uniqueness of fixed point of an integral operator, and then the sufficient condition of existence and uniqueness of solution to the problem was given on the basis of the Banach fixed point theorem. Thus our results make a theoretical foundation for the further study of the boundary value problem with p-laplacian operator.