双参数非线性方程边值问题的奇摄动

Singular perturbation of boundary value problem for nonlinear equation with two parameters

摘要: 研究一类双参数高阶半线性方程边值问题的奇摄动,讨论了摄动解随两参数的不同量级所呈现的不同性态的边界层现象.利用微分不等式证明了解的存在,并估计了余项.

Abstract: The singular perturbation of boundary value problem for a class of higher order semilinear equation with two parameters is studied.The boundary layer phenomena of different characters of perturbed solution with different quantity step of two parameters is discussed.By using differential inequalities,existence of the solution is proved,and an estimation of remainder term is given.