Oscillation and nonoscillation of third order functional differential equations

A qualitative approach is usually concerned with the behavior of solutions of a given differential equation and usually does not seek specific explicit solutions;This dissertation is the analysis of oscillation of third order linear homogeneous functional differential equations, and oscillation and nonoscillation of third order nonlinear nonhomogeneous functional differential equations. This is done mainly in Chapters II and III. Chapter IV deals with the analysis of solutions of neutral differential equations of third order and even order. In Chapter V we study the asymptotic nature of nth order delay differential equations;Oscillatory solution is the solution which has infinitely many zeros; otherwise, it is called nonoscillatory solution;The functional differential equations under consideration are:(UNFORMATTED TABLE OR EQUATION FOLLOWS) (b(ay[superscript]\u27)[superscript]\u27)[superscript]\u27 + (q[subscript]1y)[superscript]\u27 + q[subscript]2y[superscript]\u27 = 0, &(b(ay[superscript]\u27)[superscript]\u27)[superscript]\u27 + q[subscript]1y + q[subscript]2y(t - [tau]) = 0, &(b(ay[superscript]\u27)[superscript]\u27)[superscript]\u27 + qF(y(g(t))) = f(t), &(y(t) + p(t)y(t - [tau]))[superscript]\u27\u27\u27 + f(t, y(t), y(t - [sigma])) = 0, &(y(t) + p(t)y(t - [tau]))[superscript](n) + f(t, y(t), y(t - [sigma])) = 0, and &y[superscript](n) + p(t)f(t, y[tau], y[subscript]sp[sigma][subscript]1\u27,..., y[subscript]sp[sigma][subscript]n[subscript]1(n-1)) = F(t). (TABLE/EQUATION ENDS);The first and the second equations are considered in Chapter II, where we find sufficient conditions for oscillation. We study the third equation in Chapter III and conditions have been found to ensure the required criteria. In Chapter IV, we study the oscillation behavior of the fourth and the fifth equations. Finally, the last equation has been studied in Chapter V from the point of view of asymptotic nature of its nonoscillatory solutions

Oscillatory theorems of a class of even-order neutral equations

AbstractA class of even-order nonlinear neutral differential equations with distributed deviating arguments is studied, and oscillatory criteria for solutions of such equations are established

New oscillation criteria for third-order differential equations with bounded and unbounded neutral coefficients

This paper examines the oscillatory behavior of solutions to a class of thirdorder differential equations with bounded and unbounded neutral coefficients. Sufficient conditions for all solutions to be oscillatory are given. Some examples are considered to illustrate the main results and suggestions for future research are also included

Oscillation Criteria For Even Order Nonlinear Neutral Differential Equations With Mixed Arguments

This paper deals with the oscillation criteria for nth order nonlinear neutral  mixed type dierential equations

Oscillation Results for Even Order Trinomial Functional Differential Equations with Damping

In this paper, we investigate the oscillatory behavior of solutions to a certain class of nonlinear functional differential equations of the even order with damping. By using the integral averaging technique and Riccati type transformations, we prove four new theorems on the subject. Several examples are also considered to illustrate the main results

Oscillation behavior of higher order functional differential equations with distributed deviating arguments

In this thesis we consider oscillatory and nonoscillatory behavior of functional differential equations and study third and n-th order functional differential equations qualitatively. Usually a qualitative approach is concerned with the behavior of solutions of a given differential equation and does not seek explicit solutions.;This dissertation is divided into five chapters. The first chapter consists of preliminary material which introduce well-known basic concepts. The second chapter deals with the oscillatory behavior of solutions of third order differential equations and functional differential equations with discrete and continuous delay of the form (bt(a t(x\u27 t)a)\u27 )\u27+qt fxt =rt, (bt(a t(x\u27 t)a)\u27 )\u27+qt fxgt =rt , (bt(( atx\u27 t)g)\u27 )\u27+(q1 txt) \u27+q2t x\u27t=h t, (bt(a tx\u27t )\u27)\u27+ i=1mqit f(x(sit ))=ht and (bt(a tx\u27t )\u27)\u27+ cdqt,x fxst,x dx=0. In chapter three we present sufficient conditions for oscillatory behavior of n-th order homogeneous neutral differential equation with continuous deviating arguments of the form at&sqbl0; xt+pt xtt &sqbr0;n-1 \u27+dcd qt,xf xst,x dx=0. Chapter four is devoted to n-th order neutral differential equation with forcing term of the form &sqbl0;xt+ i=1mpit x(tit )&sqbr0;n +l1a bq1t,x f1(x(s1 t,x))dx +l2ab q2t,xf 2(x(s2t,x ))dx=ht . Lastly, in chapter five we present sufficient conditions involving the coefficients and arguments only for n-th order neutral functional differential equation with constant coefficient of the form &sqbl0; xt+lax t+ah+mbxt+b g&sqbr0;n =pcdx t-xdx+qc dxt+x dx

Existence of non-oscillatory solutions of a kind of first-order neutral differential equation

This paper deals with the existence of non-oscillatory solutions to a kind of first-order neutral equations having both delay and advance terms. The new results are established using the Banach contraction principle

Differential/Difference Equations

The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations