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OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN third order MIXED NEUTRAL DIFFERENCE EQUATIONS

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Acta Mathematica Scientia 2013年第1期33卷 218-226页

作者： E.THANDAPANI N.KAVITHA Ramanujan Institute for Advanced Study in Mathematics University of MadrasChennai 600 005India

The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.

关键词： oscillation third order mixed type neutral difference equation

Dependence of solutions and eigenvalues of third order linear measure differential equations on measures

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Science China Mathematics 2021年第3期64卷 479-506页

作者： Yixuan Liu Guoliang Shi Jun Yan School of Mathematics Tianjin UniversityTianjin 300354China

This paper deals with a complex third order linear measure differential equation id(y’)^(·)+ 2iq(x)y’dx + y(idq(x) + dp(x)) = λydx on a bounded interval with boundary conditions presenting a mixed aspect of the Dirichlet and the periodic problems. The dependence of eigenvalues on the coefficients p and q is investigated. We prove that the n-th eigenvalue is continuous in p and q when the norm topology of total variation and the weak*topology are considered. Moreover, the Fr′echet differentiability of the n-th eigenvalue in p and q with the norm topology of total variation is also considered. To deduce these conclusions, we investigate the dependence of solutions of the above equation on the coefficients p and q with different topologies and establish the counting lemma of eigenvalues according to the estimates of solutions.

关键词： measure differential equation third order continuity eigenvalue

High order Block Method for third order ODEs

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Computers, Materials & Continua 2021年第4期67卷 1253-1267页

作者： A.I.Asnor S.A.M.Yatim Z.B.Ibrahim N.Zainuddin School of Distance Education Universiti Sains MalaysiaUSM Penang11800Malaysia Department of Mathematics Faculty of ScienceUniversiti Putra MalaysiaSerdangSelangor Darul Ehsan43400Malaysia Department of Fundamental and Applied Sciences Universiti Teknologi PETRONASSeri IskandarPerak Darul Ridzuan32610Malaysia

Many initial value problems are difficult to be solved using ordinary,explicit step-by-step methods because most of these problems are considered *** implicit methods,however,are capable of solving stiff ordinary differential equations(ODEs)usually found in most applied *** study aims to develop a new numerical method,namely the high order variable step variable order block backward differentiation formula(VSVOHOBBDF)for the main purpose of approximating the solutions of third order *** computational work of the VSVO-HOBBDF method was carried out using the strategy of varying the step size and order in a single *** order of the proposed method was then discussed in *** advancement of this strategy is intended to enhance the efficiency of the proposed method to approximate solutions *** order to confirm the efficiency of the VSVO-HOBBDF method over the two ODE solvers in MATLAB,particularly ode15s and ode23s,a numerical experiment was conducted on a set of stiff *** numerical results prove that for this particular set of problem,the use of the proposed method is more efficient than the comparable ***-HOBBDF method is thus recommended as a reliable alternative solver for the third order ODEs.

关键词： Block method stiff ODEs third order variable step variable order

Oscillation Properties of third order Neutral Delay Differential Equations

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Applied Mathematics 2016年第15期7卷 1780-1788页

作者： Elmetwally M. Elabbasy Osama Moaaz Ebtesam Sh. Almehabresh Department of Mathematics Faculty of Science Mansoura University Mansoura Egypt Department of Mathematics Faculty of Education AL Asmarya Islamic University Zliten Libya

Oscillation criteria are established for third-order neutral delay differential equations with deviating arguments. These criteria extend and generalize those results in the literature. Moreover, some illustrating exa... 详细信息

关键词： Oscillation third order Neutral Delay Differential Equations

Stability and Boundedness of Solutions of Certain Non-Autonomous third order Nonlinear Differential Equations

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Journal of Applied Mathematics and Physics 2016年第1期4卷 149-155页

作者： Akinwale L. Olutimo Folashade O. Akinwole Department of Mathematics Lagos State University Ojo Nigeria

In this paper, by defining an appropriate Lyapunov functional, we obtain sufficient conditions for which all solutions of certain real non-autonomous third order nonlinear differential equations are asymptotically sta... 详细信息

关键词： Nonlinear Differential Equations third order Asymptotic Stability Boundedness Lyapunov Method

OSCILLATION OF third order DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

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Annals of Differential Equations 2007年第4期23卷 450-460页

作者： Liu Xiuxiang Xu Zhiting School of Mathematical Sciences South China Normal University Guangzhou 510631

In this paper we study the oscillation and asymptotic behavior of third order delay differential equations with impulses. Some new sufficient conditions which guarantee that every solution is oscillatory or converges ... 详细信息

关键词： oscillation impulses third order delay differential equations

Result on the Convergence Behavior of Solutions of Certain System of third-order Nonlinear Differential Equations

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International Journal of Modern Nonlinear Theory and Application 2016年第1期5卷 48-58页

作者： Akinwale L. Olutimo Department of Mathematics Lagos State University Ojo Nigeria

Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.

关键词： Nonlinear Differential Equations third order Convergence of Solutions Lyapunov Method