Lasota-Opial type conditions for periodic problem for systems of higher-order functional differential equations

0525395 - MÚ 2021 RIV DE eng J - Journal Article
Mukhigulashvili, Sulkhan - Půža, B.
Lasota-Opial type conditions for periodic problem for systems of higher-order functional differential equations.
Journal of Inequalities and Applications. Roč. 2020, č. 1 (2020), č. článku 155. ISSN 1029-242X. E-ISSN 1029-242X
Institutional support: RVO:67985840
Keywords : higher-order systems * periodic problem * functional differential
OECD category: Applied mathematics
Impact factor: 2.491, year: 2020
Method of publishing: Open access
https://doi.org/10.1186/s13660-020-02414-9

In the paper we study the question of solvability and unique solvability of systems of the higher-order functional differential equations u(i)((mi)) (t) = l(i)(ui+1)(t) + q(i)(t) (i = (1, n) over bar) for t is an element of I := [a, b] and u(i)((mi)) (t) = F-i(u)(t) + q(0i)(t) (i = (1, n) over bar) for t is an element of I under the periodic boundary conditions u(i)((j))(b) - u(i)((j))(a) = c(ij) (i = (1, n) over bar, j = (0, mi - 1) over bar), where u(n+ 1) = u(1), mi = 1, n = 2, c(ij) is an element of R, q(i), q(0i) is an element of L(I, R), l(i) : C-1(0) (I, R) -> L(I, R) are monotone operators and F-i are the local Caratheodory's class operators. In the paper in some sense optimal conditions that guarantee the unique solvability of the linear problem are obtained, and on the basis of these results the optimal conditions of the solvability and unique solvability for the nonlinear problem are proved.
Permanent Link: http://hdl.handle.net/11104/0309546