具有多重解的非线性Robin问题的奇摄动(英文)

Singular Perturbation of Nonlinear Robin Problem with Multiple Solution

本文利用边界层法 ,研究了具有多重解的非线性Robin问题εx″+ f(t,x)x′+ g(t,x) =0 ,0 ≤t≤ 1 ,x′( 0 ,ε) -ax( 0 ,ε) =A ,x′( 1 ,ε) +bx( 1 ,ε) =B其中ε为正的小参数 .在适当的假设下 ,我们通过给出外部解展开式系数的一般表达式 ,得到了退化问题的边值为某方程的多重根时的渐近解 ,推广了有关结果 .

In this paper, by using the boundary layer method, we study the singularly perturbed Robin boundary value problem with multiple solution for the nonlinear differential equation:εx″+f(t,x)x′+g(t,x)=0,0≤t≤1, x′(0,ε)-ax(0,ε)=A,x′(1,ε)+bx(1,ε)=B,Under the appropriate assumption, we obtain the asymptotic solution as the boundary value of the reduced problem is the multiple root of some equation, by giving the general expression of coefficients of outer solution expansion. The relative result is generalized.