title: Generalized uniqueness theorem for ordinary differential equations in Banach spaces.
abstract: We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors.forename: Ezzat R
authors.initials: ER
authors.lastname: Hassan
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors.forename: M Sh
authors.initials: MSh
authors.lastname: Alhuthali
authors.affiliation: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.
authors.forename: M M
authors.initials: MM
authors.lastname: Al-Ghanmi
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted