An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

Autor: Alberto LFC, Rabelo Marcos
Jazyk: angličtina
Rok vydání: 2010
Předmět:
Zdroj: Advances in Difference Equations, Vol 2010, Iss 1, p 496936 (2010)
Druh dokumentu: article
ISSN: 1687-1839
1687-1847
Popis: An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function to be positive in some bounded sets of the state space while the classical invariance principle assumes that . As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.
Databáze: Directory of Open Access Journals
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