Oscillation Criteria for Third-order NonlinearNeutral Dynamic Equations on Time Scales  

出　　处：《工程数学学报》2016年第2期206-220,共15页Chinese Journal of Engineering Mathematics

摘　　要：Many practical problems, such as those from electronic engineering, mechanicalengineering, ecological engineering, aerospace engineering and so on, need to bedescribed by dynamic equations on time scales, so it is important in theory andpractical significance to study these equations. In this paper, the oscillation andasymptotic behavior of third-order nonlinear neutral delay dynamic equations ontime scales are studied by using generalized Riccati transformation technique, integralaveraging methods and comparison theorems. The main purpose of this paperis to establish some new oscillation criteria for such dynamic equations. The newKamenev criteria and Philos criteria are given, and an example is considered toillustrate our main results.

关 键 词：THIRD-ORDER nonlinear dynamic equation NEUTRAL OSCILLATION CRITERION ASYMPTOTICBEHAVIOR generalized RICCATI transformation time scale 

分 类 号：O175.12[理学—数学]