On the initial value problem for two-dimensional linear functional differential systems

0347003 - MÚ 2011 RIV GE eng J - Článek v odborném periodiku
Šremr, Jiří
On the initial value problem for two-dimensional linear functional differential systems.
Memoirs on Differential Equations and Mathematical Physics. Roč. 50, - (2010), s. 1-127. ISSN 1512-0015
Grant CEP: GA ČR(CZ) GA201/06/0254; GA ČR GP201/04/P183
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: two-dimensional linear functional differential system * initial value problem * unique solvability * theorem on differential inequality
Kód oboru RIV: BA - Obecná matematika
http://www.emis.de/journals/MDEMP/vol50/abs50-1.htm

The paper of monographic type collects and supplements previous author's results. The work deals with the question on the existence and uniqueness of a solution of the initial value problem for two-dimensional systems of linear functional differential equations. Unimprovable efficient conditions sufficient for the unique solvability of the problem considered are established. The question on the existence of a constant-sign solution is also studied in detail. In other words, theorems on systems of linear functional differential inequalities (maximum principles) are discussed, which play a crucial role not only in studies of solvability of linear and non-linear problems but also for other topics related to the theory of boundary value problems (e.g., oscillation theory, asymptotic theory, etc.).
Trvalý link: http://hdl.handle.net/11104/0187881