Oscillatory behavior of second order nonlinear difference. Jump to content jump to main navigation jump to main navigation. Necessary and sufficient conditions for oscillation of second order neutral difference equations. Compared with some existing ones, our results are derived without the use of the mode transformation method and the.
Pdes are used to formulate problems involving functions of several variables, and are either solved in closed form, or used to. In simple cases, a di erence equation gives rise to an associated auxiliary equation rst explained in 7. That is, we have looked mainly at sequences for which we could write the nth term as a n fn for some known function f. In this paper we consider the existence of a positive sequence and utilize it in the capacity of integrating factor to. Neutral difference equations zhan zhou, jianshe yu and zhicheng wang department of appl. Oscillations of neutral difference equations of second.
On neutral impulsive stochastic differential equations. Examples are presented to illustrate the importance of the results. In the case of nonlinear problems, whether in differential or difference equations, it is difficult and in some cases impossible to invert the problem and obtain a suitable mapping that can be effectively used in fixed point theory to qualitatively analyze its solutions. Necessary and sufficient condition for oscillations of neutral differential equations volume 28 issue 3 m. If the number sequences and are solutions of the homogeneous equation 3 and are random numbers, then their linear combination is also a solution of 3. Second order neutral delay differential equations have applications in problems.
In this section we will consider the simplest cases. The main tool employed is the krasnoselskiis fixed point theorem for the sum of a completely continuous operator and a contraction. Existence of a nonoscillatory solution of a secondorder linear. View pdf asymptotic stability analysis of fractionalorder neutral. Research article new oscillation criteria for thirdorder. The difference between neutral and ground on the electric panel this one gives a detailed description of how the ground. Almost oscillation criteria for secondorder neutral difference.
Upper bound of numbers of terms of semicycles are determined. Stability and boundedness in nonlinear and neutral. Oscillation criteria for secondorder neutral delay. Oscillation of second order neutral type emdenfowler. Pdf convergence and divergence of the solutions of a. An application of measures of noncompactness in the. In theorem 5 and theorem 8, we have studied the oscillation criteria as well as the asymptotic behavior, where was established some sufficient conditions to ensure that every solution are either oscillates. Ocillation of first order neutral delay 3 difference equations, electric journal of qualitative of differential equations,proc. The discrete counterparts of neutral differential equations are called neutral. Introduction this article is concerned with the oscillatory behavior of neutral difference equations of the form, di. This is in contrast to ordinary differential equations, which deal with functions of a single variable and their derivatives. Difference equations differential equations to section 1.
For example, by using, a necessary and sufficient condition was obtained for the relative controllability of the neutral differential equations with delay see. Tripathy sambalpur university department of mathematics. We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form. Some riccati type difference inequalities are established for the secondorder nonlinear difference equations with negative neutral term. Pdf on oscillation of solutions to second order neutral. Oscillation criteria for secondorder neutral delay difference equations. Necessary and sufficient condition for oscillations of. Oscillation of nonlinear thirdorder delay difference. Anyone who has made a study of di erential equations will know that even supposedly elementary examples can be hard to solve. The time delays can be constant, timedependent, or statedependent, and the choice of the solver function dde23, ddesd, or ddensd depends on the type of delays in the equation. The semicycles of solutions of neutral difference equations. In this paper, we study the semicycles of solutions of neutral delay difference equation.
Neutral stochastic functional differential equations nsfdes have been initiated in and their usage in aeroelasticity was pointed out. Gomathi jawahar department of mathematics, karunya university, coimbatore641114, tamil nadu, india. Oscillation criteria of second order neutral difference equations. Linear di erence equations in this chapter we discuss how to solve linear di erence equations and give some applications. Pdf asymptotic stability in totally nonlinear neutral. Oscillation of solutions of non linear neutral difference equations with nonlinear neutral term.
In a neutral delay differential equation, the highestorder derivative of the unknown function appears both with and without delay. In this equation, if 1 0, it is no longer an differential equation and so 1 cannot be 0. Existence, uniqueness, and stability for nonlinear differentialdifference equations in the neutral case, n. In this paper, we establish some oscillation criteria of the secondorder delay difference equation. In this paper some necessary and sufficient conditions are obtained to guarantee the oscillation for bounded and all solutions of second order nonlinear neutral delay difference equations. Nonoscillation of firstorder neutral impulsive difference equations gokula nanda chhatria sambalpur university department of mathematics sambalpur, 768019, india c. Stability of linear impulsive neutral delay differential. Typically the time delay relates the current value of the derivative to the value of the solution at some prior time, but. Some new criteria for the oscillation of certain neutral difference equations of the form, di. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the gronwall integral inequality and the laplace transform method, respectively. Ddes are also called timedelay systems, systems with aftereffect or deadtime, hereditary systems, equations with deviating argument, or differentialdifference equations. Di erence equations relate to di erential equations as discrete mathematics relates to continuous mathematics.
By a solution of the neutral type difference equation e, we mean a sequence of. Global attractivity of neutral difference equations. Oscillation of third order mixed type neutral difference equations. Furthermore, by using,, the stability, oscillatory, controllability and other behaviors of solutions of delay or neutral differential equations can be achieved. Pdf oscillation and asymptotic behaviour of solutions of. Chapter 6 deals with nonoscillation and oscillation properties of scalar linear neutral differential equations. Oscillatory and asymptotic behavior of solutions of nonlinear neutraltype difference equations volume 38 issue 2 john r. Second order neutral delay difference equation is gaining interest because they are the discrete analogue of differential equations.
The world is too rich and complex for our minds to grasp it whole, for our minds are but a small part of the richness of the world. The neutral difference equations are seen as the discrete analogue of the neutral differential equations the oscillatory and asymptotic behavior of delay difference equations and neutral difference equations have been intensively studied in recent years due to its various application in. Request pdf oscillation of third order mixed type neutral difference equations in this paper, we obtain some sufficient conditions for the oscillation of all. In this paper some criteria for the oscillation of mixed type third order neutral difference equation of the form a n d n xn b n xn 1 cn xn 2 q x n n. Introduction second order neutral delay difference equation is gaining. The series focuses on the latest achievements in functional differential and difference equations, publishing contributions presented at the conferences as well as other high quality papers that outline the recent progress in functional differential and difference equations. Some properties of oscillation of second order neutral delay. Oscillation of certain neutral difference equations of.
Certain third order mixed neutral difference equations b. Some properties of oscillation of second order neutral delay difference equations. The qualitative study of such equations has, besides its theoretical interest, signi. In mathematics, delay differential equations ddes are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. Free fulltext pdf articles from hundreds of disciplines, all in one place. Recently, there has been a lot of activity concerning the oscillation and nonoscillation behavior of neutral differential and difference equations see 1, 2, 3, 4. Oscillatory and asymptotic behavior of solutions of. Pdf oscillation of nonlinear neutral type second order. A partial differential equation pde is a differential equation that contains unknown multivariable functions and their partial derivatives. This paper is concerned with the oscillation of the bounded solutions of neutral difference equation where. There are two kinds of neutral equations, one of them can be integrated leading to a term with a concentrated delay and an integral term.
Asymptotic behavior of higherorder neutral difference equations with general arguments. Exponential stability of mild solutions to impulsive. Eventually positive and bounded solutions of evenorder. Pdf the authors obtain oscillation results for the even order forced neutral difference equation. Here some oscillation results in difference equations based on the existence. A neutral delay differential equation is a differential equation in which the highest order derivative of the unknown function appears both with and without delay. Read pdf basic electrical engineering equations basic electrical engineering equations youve tried the rest, now try the best see the reallife story of. Recent progress in differential and difference equations. General solution of linear fractional neutral differential. Convergence and divergence of the solutions of a neutral hindawi. Convergence of the solutions for a neutral difference. Research article new oscillation criteria for thirdorder nonlinear mixed neutral difference equations elmetwallymohammedelabbasy, 1 magdyyosephbarsom, 1 andfaisalsalehaldheleai 2 department of mathematics, faculty of science, mansoura university, mansoura, egypt. To cope with the complexity, we reason hierarchically.
This paper is concerned with the general solution of linear fractional neutral differential difference equations. Existence of uncountably many bounded positive solutions for second order nonlinear neutral delay difference equations. One can think of time as a continuous variable, or one can think of time as a discrete variable. The present di erence equation would be presented as.
Eventually positive and bounded solutions of evenorder nonlinear neutral differential equations. Some properties of oscillation of second order neutral. Characterization of higherorder neutral difference. Pdf oscillation of a higher order neutral difference equation with a. Delay differential equations contain terms whose value depends on the solution at prior times.
In this paper, the authors using summation averaging method and an inequality present some new oscillation criteria for the second order neutral type emdenfowler delay difference equation. The established criteria significantly improve and extend related results in the literature. Properties of the solutions of linear difference equations with constant coefficients property 10. In this article we consider the existence of positive solutions of a system of periodic neutral difference equations. An application of measures of noncompactness in the investigation of boundedness of solutions of secondorder neutral difference equations, advances in difference equations, 20, pp. In the last few decades several studies on quantitative and qualitative properties of nsfdes were carried out see 4, 5, 20 and the references therein. Oscillatory and asymptotic behavior of a firstorder. Nonoscillation of firstorder neutral impulsive difference. In this paper, a collocation method based on hermite polynomials is presented for the numerical solution of the neutral functionaldifferential equations nfdes with proportional delays. Some improved criteria on exponential stability of neutral.
425 709 6 27 438 332 895 1636 1561 58 591 278 933 1350 863 482 77 621 688 926 298 195 1157 1124 1280 1392 921 864 1336 622 1129 760 468 333