一类具非线性边界条件的高阶方程的奇摄动问题

摘要

通过引入伸展变量和非常规的渐近序列{ε2}，运用合成展开法，对一类具非线性边界条件的非线性高阶微分方程的奇摄动问题构造了形式渐近解，再运用微分不等式理论证明了原问题解的存在性及所得渐近近似式的一致有效性。 j%The formal asymptotic solutions are constructed for a class of singular perturbed problems for higher order equations with nonlinear boundary value conditions by the introduction of the stretched variable and the unconventional asymptotic sequence {εj 2} and the method of composite expansions. Then the existence of solutions for the original problems and the uniform validity of the asymptotic approximations are proved by the theory of differential inequality.