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

Author:

Mukhigulashvili SulkhanORCID,Půža Bedřich

Abstract

AbstractIn the paper we study the question of solvability and unique solvability of systems of the higher-order functional differential equations $$ u_{i}^{(m_{i})}(t)=\ell _{i}(u_{i+1}) (t)+ q_{i}(t) \quad (i= \overline{1, n}) \text{ for } t\in I:=[a, b] $$ui(mi)(t)=i(ui+1)(t)+qi(t)(i=1,n) for tI:=[a,b] and $$ u_{i}^{(m_{i})} (t)=F_{i}(u) (t)+q_{0i}(t) \quad (i = \overline{1, n}) \text{ for } t\in I $$ui(mi)(t)=Fi(u)(t)+q0i(t)(i=1,n) for tI under the periodic boundary conditions $$ u_{i}^{(j)}(b)-u_{i}^{(j)}(a)=c_{ij} \quad (i=\overline{1, n},j= \overline{0, m_{i}-1}), $$ui(j)(b)ui(j)(a)=cij(i=1,n,j=0,mi1), where $u_{n+1}=u_{1} $un+1=u1, $m_{i}\geq 1$mi1, $n\geq 2 $n2, $c_{ij}\in R$cijR, $q_{i},q_{0i}\in L(I; R)$qi,q0iL(I;R), $\ell _{i}:C^{0}_{1}(I; R)\to L(I; R)$i:C10(I;R)L(I;R) are monotone operators and $F_{i}$Fi 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.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Reference20 articles.

1. Lasota, A., Opial, Z.: Sur les solutions periodiques des equations differentielles ordinaires. Ann. Pol. Math. 16, 69–94 (1964). https://doi.org/10.4064/ap-16-1-69-94

2. Mukhigulashvili, S., Lomtatidze, A.: On periodic solutions of second order functional differential equations. Mem. Differ. Equ. Math. Phys. 5, 125–126 (1995). http://eprints.iliauni.edu.ge/id/eprint/4106

3. Mukhigulashvili, S.: On periodic solutions of second order functional differential equations. Ital. J. Pure Appl. Math. 20, 29–50 (2006). http://ijpam.uniud.it/journal/abstracts.htm

4. Mukhigulashvili, S.: On a periodic boundary value problem for third order linear functional differential equations. Nonlinear Anal. 66, 527–535 (2007). https://doi.org/10.1016/j.na.2005.11.046

5. Hakl, R., Mukhigulashvili, S.: On a periodic boundary value problem for third order linear functional differential equations. Mem. Differ. Equ. Math. Phys. 41, 27–42 (2007). www.emis.de/journals/MDEMP/vol41/vol41-2.pdf

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