Existence of nontrivial solutions for discrete two-point boundary value problems

✍ Scribed by Guang Zhang; Zhilin Yang

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 159 KB
• Volume: 59
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.08.023

✦ Synopsis

In this paper, the steady-state temperature distribution of heat diffusion on multi-body is considered. Such problems can be regarded as parallel to the existence part of discrete boundary value problems. The steady-state temperature distribution at least exists a nontrivial case when all heat sources are super-linear or sublinear by studying the equivalence of solutions of the heat diffusion equation, solutions of nonlinear algebra equation, and stability point of a function. If all heat source functions are again added the odd conditions, then such a system has 2 n nontrivial solutions. By this fact, we know that the heat diffusion on multi-body may have 2 n nontrivial steady states when the initial temperature distribution is different. Similar results have not been obtained for partial differential equations.