The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analys...The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.展开更多
In this paper, we investigate some delay Cronwall type inequalities on time scales by using Cron- wall＇s inequality. Our results unify and extend some delay integral inequalities and their corresponding discrete anal...In this paper, we investigate some delay Cronwall type inequalities on time scales by using Cron- wall＇s inequality. Our results unify and extend some delay integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as handy tools in the qualitative theory of certain classes of delay dynamic equations on time scales.展开更多
Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some V...Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some Volterra-type inequalities having improper integral functionals,which are new to the literature.展开更多
In this paper results on the estimates for solutions of certain higher order finite difference equations are established. The main tool employed in our analysis is based on the applications of the discrete inequality ...In this paper results on the estimates for solutions of certain higher order finite difference equations are established. The main tool employed in our analysis is based on the applications of the discrete inequality which provides an explicit bound on the unknown function.展开更多
In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the soluti...In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.展开更多
文摘The aim of this paper is to establish some new discrete inequalities in two independent variables which can be used as handy tools.in the theory of certain fourth order partial finite difference equations. The analysis used in the proof is elementary and the results established provide new estimates for these types of inequalities.AMS (MOS) Subject Classification (1991 ): Primary 26D15.
基金Supported by the National Natural Science Foundation of China(No.10971018)the Natural Science Foundation of Shandong Province(No.Y2009A06)+3 种基金China Postdoctoral Science Foundation Funded Project(No.20080440633)Shanghai Postdoctoral Scientific Program(No.09R21415200)the Project of Science and Technology of the Education Department of Shandong Province(No.J08LI52)the Doctoral Foundation of Binzhou University(No.2006Y01)
文摘In this paper, we investigate some delay Cronwall type inequalities on time scales by using Cron- wall＇s inequality. Our results unify and extend some delay integral inequalities and their corresponding discrete analogues. The inequalities given here can be used as handy tools in the qualitative theory of certain classes of delay dynamic equations on time scales.
文摘Explicit bounds on bounded solutions to a new class of Volterra-type linear and nonlinear discrete inequalities involving infinite sums are established. These inequalities can be viewed as discrete analogues of some Volterra-type inequalities having improper integral functionals,which are new to the literature.
文摘In this paper results on the estimates for solutions of certain higher order finite difference equations are established. The main tool employed in our analysis is based on the applications of the discrete inequality which provides an explicit bound on the unknown function.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order difference equations.With the aid of the discrete inequality,we obtain some sufficient conditions which ensure that all the solutions to the equation are some high order of infinities,and also that some conditions which guarantee that every oscillatory solution to the equation has the property that the i order L operator of it tends to infinity when its independent variable tends to zero.
