某一类型积分微分方程非线性边值问题的奇摄动

Singular perturbation of Volterra type integro-differential equation for nonlinear boundary value problems

利用微分不等式理论研究了二阶Volterra型积分微分方程非线性边值问题的解的存在性.在适当条件下,建立了解的渐近展开.构造具体的上下解,得到了解的存在性和解的一致有效估计.这种技巧为奇摄动边值问题的存在性和解的一致有效估计的研究提出了新的思路.

By means of differential inequality theories, the existence of solution for nonlinear boundary value problem of Volterra type equation is studied. Based on the suit condition, the asymptotic expand of solution is established. Specific upper and lower solutions are constructed, the existence and uniformly estimation of solution is obtained. The result shows that is seems to be new to apply these techniques to solving the existence and uniqueness of singularly perturbed boundary problem.