On the Solvability of the Periodic Problem for Systems of Linear Functional Differential Equations with Regular Operators (original) (raw)
Russian Mathematics, 2011
We consider first-order systems of linear functional differential equations with regular operators. For families of systems of two equations we obtain the general necessary and sufficient conditions for the unique solvability of a periodic boundary-value problem. For families of systems of n linear functional differential equations with cyclic matrices we obtain effective necessary and sufficient conditions for the unique solvability of a periodic boundary-value problem.
Periodic solutions of first order functional differential equations
2011
We study the existence of T-periodic solutions of some first order functional differential equations. Several existence criteria are established for our problems; in particular, we obtain conditions for the existence of multiple (even infinitely many) T-periodic solutions of one of the problems. Examples are also included to illustrate our results.
Periodic solutions for functional–differential equations of mixed type
Journal of Mathematical Analysis and Applications, 2007
In this paper we study the existence of ω-periodic solutions for some functional-differential equations of mixed type. Among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities. We use here the coincidence degree theory of Mawhin.
submitted
We investigate criteria for the uniqueness of (mild) periodic solutions to periodic linear functional differential equations with finite delay in Banach spaces. Its arguments are carried out by materializing the theory of seni-Fredholm operators mathrmadotmathrmnmathrmd\mathrm{a}\dot{\mathrm{n}}\mathrm{d}mathrmadotmathrmnmathrmd by using the standard way. In particular, two sufficient conditions ensuring the uniqueness of periodic solutions are obtained : they are independent of each other. [28][29][30][31][32][33][34][35][36]