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Comparison Theorems in Delay Differential Equations in a Critical State and Applications
Author(s) -
Yu J. S.,
Tang X. H.
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610700001599
Subject(s) - delay differential equation , mathematics , oscillation (cell signaling) , differential equation , ordinary differential equation , order (exchange) , state (computer science) , mathematical analysis , oscillation theory , first order , differential algebraic equation , algorithm , genetics , finance , economics , biology
First, two comparison theorems are established between the first order delay differential equation x ′( t )+ p ( t ) x (τ( t ))=0, t ⩾ t 0 (*) and two related second order ordinary differential equations in the case when∫ τ ( t ) t p ( s ) d s ⩾ 1 e .( * * )Next, by using these comparison theorems some new oscillation and non‐oscillation criteria are given for (*) under condition (**). As a consequence, an open problem by Elbert and Stavroulakis is completely solved.