TY - JOUR
T1 - Refined Approximations of the Solutions of a Coupled System with Turning Points
AU - Harris, W. A.
AU - Shao, S.
PY - 1991/1/1
Y1 - 1991/1/1
N2 - 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.
AB - 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.
UR - https://engagedscholarship.csuohio.edu/scimath_facpub/333
U2 - 10.1016/0022-0396(91)90067-J
DO - 10.1016/0022-0396(91)90067-J
M3 - Article
VL - 92
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -