Nonoscillation of First-Order Dynamic Equations with Several Delays

Advances in Difference Equations

Elena Braverman¹  Baak Karpuz² 

[1] Department of Mathematics and Statistics, University of Calgary, Calgary, Canada, T2N 1N4;Department of Mathematics, Faculty of Science and Arts, ANS Campus, Afyon Kocatepe University, Afyonkarahisar, Turkey

关键词: Difference Equation;    Fundamental Solution;    Comparison Theorem;    Delay Differential Equation;    Delay Function;   

DOI  :  10.1155/2010/873459

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

For dynamic equations on time scales with positive variable coefficients and several delays, we prove that nonoscillation is equivalent to the existence of a positive solution for the generalized characteristic inequality and to the positivity of the fundamental function. Based on this result, comparison tests are developed. The nonoscillation criterion is illustrated by examples which are neither delay-differential nor classical difference equations.

【 授权许可】

CC BY