Singular perturbation of BVP for third-order nonlinear VDE

Abstract

Abstract: The singularly perturbations for the vector boundary value problem of nonlinear third-order ordinary differential equations were studied. Under certain conditions, the given differential equation was transformed into a diagonalized system, and then the equivalent integral equations was solved. By using the method of succesive approximation and the theorem of fixed point, the existence of the solution of singular perturbation problem was proved and the asymptotic estimation was obtained. Finally, several examples of application were given.

Key words: singular perturbation, boundary value problem, nonlinear vector equation, diagonalization method

CLC Number:

O175

LIN Su-rong, NI Ming-Kang. Singular perturbation of BVP for third-order nonlinear VDE[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(1): 138-150.

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