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Journal of the London Mathematical Society 2001 63(1):188-204; doi:10.1112/S0024610700001599
© 2001 by London Mathematical Society
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© The London Mathematical Society

Comparison Theorems in Delay Differential Equations in a Critical State and Applications

J. S. Yu and X. H. Tang

Department of Applied Mathematics, Hunan University Changsha, Hunan 410082, China, jsyu{at}mail.hunu.edu.cn
Department of Applied Mathematics, Central South University of Technology Changsha, Hunan 410083, China

Received 12 August 1999. Revision received 17 April 2000.

First, two comparison theorems are established between the first order delay differential equation

x'(t)+p(t)x({tau}(t))=0, t≥t0 (*)

and two related second order ordinary differential equations in the case when


Formula

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.


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