Lin, Surong; Ni, Mingkang Singular perturbations of BVP for third-order nonlinear VDE. (Chinese. English summary) Zbl 1265.34059 J. East China Norm. Univ., Nat. Sci. Ed. 2012, No. 1, 138-150 (2012). Summary: Singularly perturbed vector boundary value problems of nonlinear third-order ordinary differential systems are studied. Under certain conditions, the given differential system is transformed into a diagonalized system, and then the equivalent integral equation is solved. By using the method of successive approximation and a fixed point theorem, the existence of a solution is proved and the asymptotic estimation is obtained. Finally, several examples are given. MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms 34A45 Theoretical approximation of solutions to ordinary differential equations 47N20 Applications of operator theory to differential and integral equations 34E05 Asymptotic expansions of solutions to ordinary differential equations Keywords:singular perturbation; boundary value problem; nonlinear vector differential equation; diagonalization method PDFBibTeX XMLCite \textit{S. Lin} and \textit{M. Ni}, J. East China Norm. Univ., Nat. Sci. Ed. 2012, No. 1, 138--150 (2012; Zbl 1265.34059)