Jiang Fu-ru. On the Boundary Value Problems for Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1991, 12(2): 108-117.
 Citation: Jiang Fu-ru. On the Boundary Value Problems for Ordinary Differential Equations with Turning Points[J]. Applied Mathematics and Mechanics, 1991, 12(2): 108-117.

# On the Boundary Value Problems for Ordinary Differential Equations with Turning Points

• Publish Date: 1991-02-15
• In this paper, we consider the boundary value problems of the form ey"-f(x,e)y'+g(x,e)y=0(-a≤x≤b,0<ε≤1)y(-a)=a,y(b)=β where f(x,0) has several and multiple zeros on the interval [-a,b]. The conditions for exhibiting boundary and interior layers are given, and the corresponding asymptotic expansions of solutions are constructed.
•  [1] Wasow,W.,Asymptotic Expansions for Ordinary Differential Equations,Wiley(Interscience),New York(1965). [2] Watts,A.M.,A singular perturbation problem with a turning point,Bull.Australian Math.Soc.,5(1971),61-73. [3] Ackerberg,R.C.and R.E.O'Malley,Jr.,Boundary layer problems exhibiting resonance,Stud.Appl.Math.,49(1970),277-295. [4] O'Malley,R.E.,Jr.,Introduction to Singular Perturbations,Academic Press,New York(1974). [5] Matkowskey,B.J.,On boundary layer problems exhibiting resonance.SIAM Rev.,17(1975),82-100. [6] 江福女,关于常微分方程转点问题共振的必要条件,应用数学和力学,10,4(1989),277-284. [7] De Groen,P.P.N.,The singularly perturbed turning point problem:a spectral approach.Singular Perturbation and Asymptotic,Academic Press,New York(1980),149-172. [8] Skinner,L.A.,Uniform solution of boundary layer problems exhibiting resonance,SIAM J.Appl.Math.,47,2(1987),225-231.

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