In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe...In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.展开更多
Some new oscillation criteria are given for a second order nonlinear difference equation with continuous variable. Our results generalize and improve the recent criteria of Zhang Z.G., Bi P. and Chen J.F..
： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
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 imp...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.展开更多
Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend ...Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend some known oscillation results in the literature.展开更多
Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improv...Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.展开更多
In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and...In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.展开更多
基金supported by the National Natural Science Foundation of China(12071491,12001113)。
文摘In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.
文摘Some new oscillation criteria are given for a second order nonlinear difference equation with continuous variable. Our results generalize and improve the recent criteria of Zhang Z.G., Bi P. and Chen J.F..
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘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.
文摘Some new oscillation criteria are given for forced second order differential equations with mixed nonlinearities by using the generalized variational principle and Riccati technique. Our results generalize and extend some known oscillation results in the literature.
文摘Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.
基金Supported by Guangdong Province Teaching Reform Project in Higher Education(GDJG20142396)Higher School Characteristic Innovation Project(research in education)of Guangdong Province in 2014
文摘In this paper, the oscillation of a class of nonlinear even order neutral partial functional differential equations with continuous distributed delay is studied. By employing the generalized Riccati transformation and the technique of differential inequalities, some new sufficient conditions are obtained for the oscillation of the partial differential equations under Robin boundary value conditions. The results generalize some of the previous results.
基金Supported by the Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)the Hunan Province Science and Technology Project(2012FJ3107)
基金Supported by the Natural Science Foundation of Hunan Province(12JJ6006)Hunan Province Science and Technology Project(2012FJ3107)the National Natural Science Foundation of China(11071222)
