On a boundary value problem for first-order scalar functional differential equations

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

“…The main goal of this paper is to establish new general condition sufficient for the unique solvability of the non-local non-linear boundary-value problem (2) for the non-linear functional differential equations (1). For non-linear functional differential systems determined by operators that may be defined on the space of the absolutely continuous functions only, we prove several new theorems close to some results of [2,5,7,14,15,13,12].…”

“…The main goal of this paper is to establish new general condition sufficient for the unique solvability of the non-local non-linear boundary-value problem (2) for the non-linear functional differential equations (1). For non-linear functional differential systems determined by operators that may be defined on the space of the absolutely continuous functions only, we prove several new theorems close to some results of [2,5,7,14,15,13,12].The main theorems established here generalize some recent results from [5,14,3,6,15] and are proved by using an abstract theorem from [9].2000 M a t h e m a t i c s S u b j e c t C l a s s i f i c a t i o n: Primary 34K10. K e y w o r d s: non-linear boundary-value problem, functional differential equation, non-local condition, unique solvability, differential inequality.…”

Component-wise positivity of solutions to periodic boundary problem for linear functional differential system

“…Then the technique of analysis of the first order scalar functional differential equations, developed, for example, in the works [13,14], is used. On this basis we prove assertions of Section 3.…”

On the solvability of the periodic boundary value problem for a linear functional differential equation

“…Условиям разрешимости периодической краевой задачи для различных видов функци-онально-дифференциальных уравнений за последние годы было посвящено значительное чис-ло работ [1][2][3][4][5][6][7][8][9][10][11][12]. В частности, для функционально-дифференциальных уравнений первого [1,3], второго [5], третьего [11] порядков получены неулучшаемые условия однозначной разрешимо-сти.…”

“…Для обыкновенных дифференциальных уравнений различные неулучшаемые условия од-нозначной разрешимости периодической задачи были получены, например, в работах [16,17,18], причем результаты работы А. Лясоты и З. Опяля [16] послужили основой для многих дальнейших обобщений, в частности, [1][2][3][4][5][6][7][8][9][10][11][12]17]. § 2 .…”