Geng, Fazhan; Cui, Minggen Solving a nonlinear system of second order boundary value problems. (English) Zbl 1113.34009 J. Math. Anal. Appl. 327, No. 2, 1167-1181 (2007). A method is presented to obtain the analytical and approximate solution of a nonlinear system of second order boundary value problems. The analytical solution is represented in the form of a series in the reproducing kernel space. Reviewer: Jiaqi Mo (Wuhu) Cited in 107 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:analytical solution; nonlinear second order differential system; reproducing kernel PDF BibTeX XML Cite \textit{F. Geng} and \textit{M. Cui}, J. Math. Anal. Appl. 327, No. 2, 1167--1181 (2007; Zbl 1113.34009) Full Text: DOI OpenURL References: [1] Thompson, H.B.; Tisdell, C., Systems of difference equations associated with boundary value problems for second order systems of ordinary differential equations, J. math. anal. appl., 248, 333-347, (2000) · Zbl 0963.65081 [2] Cheng, Xiyon; Zhong, Chengkui, Existence of positive solutions for a second order ordinary differential system, J. math. anal. appl., 312, 14-23, (2005) · Zbl 1088.34016 [3] Thompson, H.B.; Tisdell, C., Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations, Appl. math. lett., 15, 6, 761-766, (2002) · Zbl 1003.39012 [4] Thompson, H.B.; Tisdell, C., The nonexistence of spurious solutions to discrete, two-point boundary value problems, Appl. math. lett., 16, 1, 79-84, (2003) · Zbl 1018.39009 [5] Mawhin, J.; Tisdell, C., A note on the uniqueness of solutions to nonlinear, discrete, vector boundary value problems, Nonlinear anal. appl., 1-2, 789-798, (2003), (to V. Lakshmikantham on his 80th birthday) · Zbl 1053.39032 [6] Valanarasu, T.; Ramanujam, N., An asymptotic initial value method for boundary value problems for a system of singularly perturbed second-order ordinary differential equations, Appl. math. comput., 147, 227-240, (2004) · Zbl 1040.65071 [7] Li, Chunli; Cui, Minggen, The exact solution for solving a class nonlinear operator equations in the reproducing kernel space, Appl. math. comput., 143, 2-3, 393-399, (2003) · Zbl 1034.47030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.