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 established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [...Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [11].We remove some assumptions that are required for the related results in the previous papers,thus our results generalize and improve many known conclusions.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
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..
By using a generalized Riccati transformation, we establish some new oscillation criteria which improve and generalize some known criteria in literatures.
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
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.
基金supported by the National Natural Science Foundation of China (10771118)the Fund of Subject for Doctor of Ministry of Education (20103705110003)the Natural Science Foundations of Shandong Province (ZR2009AM011 and ZR2009AL015)
文摘Some new oscillation criteria are established for a second order neutral partial functional differential equation.Assumptions in our theorems are less restrictive,also the proofs are simpler than those in Li and Cui [11].We remove some assumptions that are required for the related results in the previous papers,thus our results generalize and improve many known conclusions.
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.
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..
文摘By using a generalized Riccati transformation, we establish some new oscillation criteria which improve and generalize some known criteria in literatures.
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.
