In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower...In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower solution a with β a.展开更多
A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed s...A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.展开更多
文摘In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem in the presence of an upper solution βand lower solution a with β a.
基金Project supported by the National Science Fund for Distinguished Young Scholars of China(No.51125019)the National Natural Science Foundation of China(No.11171237)the Scientific Research Fund of Sichuan Provincial Education Department(No.11ZA024)
文摘A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.
