一类强非线性方程奇摄动Robin问题解的渐近性态

Asymptotic Behavior of Singular Perturbed Solution of Robin Problems for a Class of Strongly Nonlinear Equations

用奇摄动理论研究一类强非线性方程的Robin问题,讨论了边界条件对问题解渐近性态的影响.在适当的条件下,相应于边界值的不同取值范围,得出了解的渐近表达式.对一类非线性问题的研究提供了一种得到渐近解的有效方法.

By means of the theory of singularly perturbation, Robin problems of a class of strongly nonlinear equations are considered. The infection of the boundary condition on the asymptotic behavior of the solution of the problem is studied. Under suitable conditions and according to the different regions of the boundary values, the asymptotic expansions of the solution are obtained simply and conveniently. This paper provides a valid method to obtain asymptotic solution for a class of nonlinear problems.