三阶微分差分方程非线性边值问题的存在性与唯一性

Existence and Uniqueness of Solutions for Nonlinear Boundary Value Problems of Third Order Differential-Difference Equation

利用微分不等式技巧研究了一类三阶微分差分方程的非线性边值问题,以二阶边值问题的已知结果为基础,建立了Volterra型积分微分差分非线性方程解的存在性,利用反证法获得了解的唯一性.同时,构造适当的上下解,得到了三阶微分差分方程解的存在性与唯一性.结果表明:这种技巧为其它边值问题的研究提出了崭新的思路.

A class of nonlinear boundary value problems of third order differential-difference equation was studied by differential inequality theories.Based on the given results of second order boundary value problem,the existence of the solutions of nonlinear differential-difference equation of Volterra type integro-differential-difference nonlinear equation were established.The uniquess of solution was obtained by applying disproof method.The suit upper and lower solutions were constructed,and existence and unique of solutions of third order differential-difference equation were obtained.The result shows that it seems new to apply these techniques to solve other boundary value problems.