摘要
本文研究了一类奇摄动二阶非线性边值问题: Ey＇＇—f(x,y,y＇)=0.0<x<1, y(0)—Eay＇(0)=A.a≥0. y(1)+Eby＇(1)=B.b≥0. 在议定的条件下,利用微分不等式理论。证明了该问题存在一个解y(?)(x)∈C^2[0,1],且成立: y(?)(x)-y_0(x)=O(C_1(1+C_1x/∈)~1)+O(C_2(1+C_2(1-x)/∈)~1)=O(∈), 0≤x≤1,〈∈〈1, 其中C_1,C_2为非负常数,而y_0(x)∈C^2[0,1]满足f_Z(x,y_0,z)=0。
A class of singularly perturbed second nonlinear boundary value problems
of differential equation
εy”--f(x,y,y’)=0, O<x<1,
y(0)- εay’(O)=A, a≥0,
y(1)+ εby’(1)=B, b≥0.
is considered.Under certain conditions,using the differential inequality there
exists a solution y,(x)∈C^2[0, 1].And the solution y,(x)holds
y,(x)—y_0(x)=O(C_1(1+C_1x/ε^(-1))+O(C_2(1+C_2(1—x)/ε)^(-1))+O(ε),
O≤x≤1, O<ε<1,
where C_1 and C_2 are nonnegative constants,while y_0(x)∈C^2[0,1] satisties f
(x,y_0,z)=0.
基金
国家自然科学基金资助课题
关键词
奇摄动
非线性
边值问题
微分方程
Singular perturbation
Nonliear boundary value problem
Differential inequality
