Differential Inequalities for One Component of Solution Vector for Systems of Linear Functional Differential Equations

Autor: Domoshnitsky Alexander
Jazyk: angličtina
Rok vydání: 2010
Předmět:
Zdroj: Advances in Difference Equations, Vol 2010, Iss 1, p 478020 (2010)
Druh dokumentu: article
ISSN: 1687-1839
1687-1847
Popis: The method to compare only one component of the solution vector of linear functional differential systems, which does not require heavy sign restrictions on their coefficients, is proposed in this paper. Necessary and sufficient conditions of the positivity of elements in a corresponding row of Green's matrix are obtained in the form of theorems about differential inequalities. The main idea of our approach is to construct a first order functional differential equation for the th component of the solution vector and then to use assertions about positivity of its Green's functions. This demonstrates the importance to study scalar equations written in a general operator form, where only properties of the operators and not their forms are assumed. It should be also noted that the sufficient conditions, obtained in this paper, cannot be improved in a corresponding sense and does not require any smallness of the interval , where the system is considered.
Databáze: Directory of Open Access Journals
Externí odkaz: