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ON UNIFORMLY VALID ESTIMATE OF SOLUTIONS TO SINGULAR PERTURBATION ROBIN BOUNDARY VALUE PROBLEM
王怀忠, 周钦德
数学物理学报(英文版). 1988 (4):
389-398.
In this paper we study the Robin boundary value problem with a small parameter εy"=f(t, y, ω(ε)y', ε), a0y(0) +b0y'(0)=ξ(ε), a1y(1)+b1y'(1)=η(ε), where the function ω(ε) is continuous on ε ≥ 0 with ω(0)=0. Assuming all known functions are suitably smooth, f satisfies Nagumo's condition, fy>0, ai2-bi2≠0, (-1)iaibi ≤ 0 (i=0, 1) and the reduced equation 0=f(t, y, 0, 0) has a solution y(t) (0 ≤ t ≤ 1), we prove the existence and the uniqueness of the solution for the boundary value problem and givo an asymptotic expansion of the solution in the power ε1/2 which is uniformly valid on 0 ≤ t ≤ 1.
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