Variational principle for a three-point boundary value problem


Hong-Yan Liu - School of Fashion Technology, Zhongyuan University of Technology, No. 41 Zhongyuan Road (M), 450007 Zhengzhou, 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.


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.