二阶Hammerstein型线性边值问题的积分微分差分方程

Linear Boundary Value Problems of Second Order Hammerstein Type Integro-differential-difference Equation

利用微分不等式技巧研究了一类二阶非线性Hammerstein型积分微分差分方程的线性边值问题。以二阶边值问题的已知结果为基础,建立了微分差分非线性方程解的存在性,以及Hammerstein型线性方程解的唯一性。在上下解存在的条件下,构造迭代序列,由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。结果表明:这种技巧也为其它边值问题的研究提出了一种思路。

The linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were studied by means of differential inequality theories. Based on the given results of second order boundary value problem, the existence of solutions of nonlinear differential-difference equation and unique of solutions of Hammerstein type integro-differential-difference linear equation were established because Harnmerstein linear equation featured only one solution. Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method. The result expatiated that this appraoch seemed new to apply these technique to solving other boundary value problems.