【摘要】 在适当的条件下,用边界摄动理论和微分不等式技巧,研究了一类摄动不仅发生在方程而且同时发生在内部点和边界处的非线性奇摄动问题.利用改进以往相关文献中辅助函数的构造证明了解的存在性,得到了原问题解以及解的导函数的任意阶一致有效渐近表达式.本文的结果丰富和推广了相关成果.更多还原

【Abstract】 Under appropriate conditions,using the boundary perturbation theory and the technique of differential inequalities,a class of nonlinear singularly perturbed problems with perturbation not only arising in the equation but also arising in interior points and boundary points is considered.The existence of solution is proved by improving the structure of auxiliary functions in the literature.The uniformly valid asymptotic expansion of the solution and its derivation for arbitrary order are obtained.The conclusion in this paper richens and improves some early results.更多还原