On fuzzy boundary value problems
- 作者：Minghao Chen ; Congxin Wu ; Xiaoping Xue ; Guoqing Liu
- 关键词：Parametric representation of fuzzy number ; Fuzzy differential equation ; Two-point boundary value problem ; Green’ ; s function ; Integration by parts
- 刊名：Information Sciences
- 出版年：2008
- 期刊代码：62_00200255
- 类别：cp
- 出版时间：1 April 2008
- 卷：178
- 期：7
- 页码：1877-1892
- 文件大小：253 K
摘要
The statement that a two-point boundary value problem of fuzzy differential equation is equivalent to a fuzzy integral equation was pointed out by Lakshmikantham et al. and O’Regan et al. Recently Bede gave a counterexample to show that this statement does not hold and he also argued that in many cases two-point boundary value problems have no solutions. Under a new structure and certain conditions we show that a two-point boundary value problem is equivalent to a fuzzy integral equation. We also prove the existence of solutions to the two-point boundary value problem. In some sense, this is an amendment to results of Lakshmikantham et al. and O’Regan et al., and it is an answer to one of Bede’s problems.