一类双参数高阶拟线性非局部方程奇摄动解(英文)

The Singularly Perturbed Solution for a Class of Quasilinear Nonlocal Problem for Higher Order with Two Parameters

研究了一类高阶非局部奇摄动边值问题.在适当的条件下,首先,利用渐近展开方法,构造了退化解和外部解.于是利用伸长变量的变换,构造了具有指数型衰减的初始层项.最后,利用微分不等式理论,证明了原边值问题解的存在性和一致有效性.

A class of singularly perturbed initial value problem of nonlocal equation is considered.Under suitable conditions,using the asymptotic expansion method,the reduced solution and outer solution are constructed.Then,using the transformation of stretched variable,the initial layer corrective terms are obtained which possesses exponential degeneration.Finally,using the theory of differential inequalities the existence,uniform validity of solution for the original initial value problem is proved.