On Periodic Boundary-Value Problems for Systems of Functional-Differential Equations
- 3 Downloads
We obtain necessary and sufficient conditions for the existence of a unique solution to a periodic boundary-value problem for all systems of first-order functional-differential equations from a given family of systems. Families of systems of functional-differential equations are detrmined by the norms of positive functional operators of equations of the system. The verification of necessary and sufficient conditions of the existence of a unique periodic solution for all systems from a given family consists of the verification of positivity of a finite number of a real-valued functions defined on a finite-dimensional set.
Keywords and phrasesfunctional-differential equation boundary-value problem exact solvability condition periodic boundary-value problem
AMS Subject Classification34K06 34K10 34K13
Unable to display preview. Download preview PDF.
- 3.E. I. Bravyi, “On the solvability of the periodic boundary-value problem for systems of functional-differential equations with cyclic matrices,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., No. 10, 17–27 (2011).Google Scholar
- 4.E. I. Bravyi, “On the solvability of the periodic problem for systems of linear functional differential equations with regular operators,” Electron. J. Qual. Theory Differ. Equ., No. 59, 1–17 (2011).Google Scholar
- 5.J. D. Cao and J. Q. Lu, “Adaptive synchronization of neural networks with or without time-varying delay,” Chaos, 16, No. 013133 (2006).Google Scholar