具有非线性三点边值条件的三阶奇摄动边值问题

讨论了三阶非线性微分方程三点非线性边值问题的奇摄动.首先利用积分算子和微分不等式技巧,以二阶边值问题的已知结果为基础,建立了积分微分非线性方程解的存在性,在上下解存在的条件下,构造迭代序列,得到了三阶非线性边值问题的解的存在性,同时利用反证法,得到了解的惟一性;其次在适当的条件下,通过构造具体的上下解的渐近估计.结果表明,这种技巧为其他三阶奇摄动边值问题的研究提出了一种新的思路.

Third order singular perturbation boundary value problem with nonlinear three-point boundary value condition

In this paper,singular perturbation of three-point boundary value problem for third order nonlinear equation was studied,by using Volterra type integral operator and differential inequality techniques.Based on the given results of second order boundary value problem,the existence of solutions of nonlinear differential equation and unique of solutions of integro-differential nonlinear equation were established.Under the proper condition of upper and lower solution,iteration sequences were constructed,and existence of boundary value problems on third order nonlinear equation were obtained,and uniqueness were obtained by applying disproof method.The upper and lower solutions were constructed under specific condition,and asymptotic was established.The use of these techniques to study for these kinds of third-order singularly perturbed boundary value problems seems to be new.