SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS
LIN Su-rong1, TIAN Gen-bao2, LIN Zong-chi3
1. Mathematical Section, Fujian Broadcasting TV University, Fuzhou 350003, P. R. China; 2. Department of Mathematics, Shanghai Railroad University, Shanghai00333, P. R. China; 3. Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China
LIN Su-rong;TIAN Gen-bao;LIN Zong-chi. SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS. Applied Mathematics and Mechanics (English Edition), 2001, 22(2): 229-236.
[1] Nayfeh A H.Perturbation Methods[M].New York:Wiley,1973. [2] O’Malley R E.Introduction to Singular Perturbations[M].New York:Academic,1974. [3] Chang K W,Howes F A.Nonlinear Singular Perturbation Phenomena:Theory and Application[M].New York:Springer-Verlag,1984. [4] LIN Zong-chi,ZHOU M ing-ru.Perturbation Methods in Applied Mathematics[M].Nanjing:Jiangsu Education Press,1995.(in Chinese) [5] O’Malley R E.Two parameters singular perturbation problems for second order equations[J].J Math Mech,1967,16(10):1143-1163. [6] O’Malley R E.Singular perturbations of boundary value problems for linear ordinary differential equations involving two parameters[J].J Math Anal Appl,1967,19:291-308. [7] ZHANG Han-lin.On the singular perturbation of a nonlinear ordinary differential equation with two parameters[J].Applied Mathematics and Mechanics(English Edition),1989,10(5):471-480. [8] MIAO Shu-mei.The singularly perturbed boundary value problems for second-order ordinary differential equations with two small parameters[J].Acta Scientiarum Naturalium Universitatis Jilinensis,1991,(4):37-41.(in Chinese) [9] ZHOU Ya-li,LIN Zong-chi.Singular perturbation of boundary value problem for third-order nonlinear differential equation with two small parameters[J].Journal of Fujian Normal University(Natural Science),1997,13(3):19-22.(in Chinese) [10] Gene A Kleasen.Differential inequalities and existence theorems for second and third order boundary value problems[J].J Differential Equations,1971,10:529-533.