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Full-Text Articles in Physical Sciences and Mathematics
Refined Approximations Of The Solutions Of A Coupled System With Turning Points, W. A. Harris, S. Shao
Refined Approximations Of The Solutions Of A Coupled System With Turning Points, W. A. Harris, S. Shao
Mathematics and Statistics Faculty Publications
We present in this paper the asymptotic behavior of solutions of a boundary value problem for a coupled system of differential equations u″ = ν, εν″ + f(u, u′)ν′ - g(x, u, u′)ν = 0 on a compact interval I, where f(u, u′) has turning points in I. We provide upper and lower solutions, β(x, ε) and α(x, ε), respectively, which bound solutions, exhibiting boundary layer and interior layer behavior, for which limε → 0+ {β(x, ε) - α(x, ε)} = 0 uniformly on I.