数学物理学报(英文版) ›› 1997, Vol. 17 ›› Issue (2): 167-179.
史玉明1, 高灿柱2
Shi Yuming1, Gao Canzhu2
摘要: In the present paper, the singular perturbations for the higher-order scalarnonlinear boundary value problem
ε2y=f(t,ε,y,y',…,y(n-2),εy(n-1)),t∈[0,1] H1(y(0,ε),…,y(n-3)(0,ε),εy(n-2))(0,ε),εy(n-1))(0,ε),ε)=0,H2(y(0,ε),…,y(n-1)(0,ε),y(1,ε),…,y(n-1)(1,ε),ε)=0 are studied, where ε > 0 is a small parameter, n ≥ 2. Under some mild assumptions,we prove the existence and local uniqueness of the perturbed solution and give out the uniformly valid asymptotic expansions up to its nth-order derivative function by employing the Banach/Picard fixsed-point theorem. Then the existing results are extended and improved.