Variational principle for a three-point boundary value problem

Volume 9, Issue 8, pp 5169--5174 http://dx.doi.org/10.22436/jnsa.009.08.02

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Authors

Hong-Yan Liu - School of Fashion Technology, Zhongyuan University of Technology, No. 41 Zhongyuan Road (M), 450007 Zhengzhou, China. - National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, 215123 Suzhou, China. Ji-Huan He - National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, 215123 Suzhou, China. Zhi-Min Li - Rieter (China) Textile Instrument Co., 1068 West Tianshan Road, 200335 Shanghai, China.

Abstract

A variational principle is established for a three-point boundary value problem. The stationary condition includes not only the governing equation but also the natural boundary conditions. The paper reveals that not every boundary condition adopts a variational formulation, and the existence and uniqueness of the solutions of a three-point boundary value problem can be revealed by its variational formulation.

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Keywords

• Variational theory
• boundary value problem
• semi-inverse method
• natural boundary condition.

MSC

•  34B10
•  34B15
•  35A15

References

• [1] U. Akcan, N. A. Hamal, Existence of concave symmetric positive solutions for a three-point boundary value problem, Adv. Difference Equ., 2014 (2014), 12 pages


• [2] F. Geng, Solving singular second order three-point boundary value problems using reproducing kernel Hilbert space method, Appl. Math. Comput., 215 (2009), 2095--2102


• [3] J. H. He, Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos Solitons Fractals, 19 (2004), 847--851


• [4] J. H. He, Variational approach to impulsive differential equations using the semi-inverse method, Zeitschrift für Naturforschung A, 66 (2011), 632--634


• [5] J. H. He, Asymptotic methods for solitary solutions and compactons, Abstr. Appl. Anal., 2012 (2012), 130 pages


• [6] Y. Hu, J. H. He, On fractal space-time and fractional calculus, Thermal Sci., 20 (2016), 773--777


• [7] Z. Jia, M. Hu, Q. Chen, Variational principle for unsteady heat conduction equation, Thermal Sci., 18 (2014), 1045--1047


• [8] X. W. Li, Y. Li, J. H. He, On the semi-inverse method and variational principle, Thermal Sci., 17 (2013), 1565--1568


• [9] M. Mohamed, B. Thompson, M. S. Jusoh, First-order three-point boundary value problems at resonance, J. Comput. Appl. Math., 235 (2011), 4796--4801


• [10] Y. P. Sun, Existence of triple positive solutions for a third-order three-point boundary value problem, J. Comput. Appl. Math., 221 (2008), 194--201


• [11] X. C. Zhong, Q. A. Huang, Approximate solution of three-point boundary value problems for second-order ordinary differential equations with variable coefficients, Appl. Math. Comput., 247 (2014), 18--29