Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments

Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form $$r(t)\psi(x(t))|z'(t)|^{\alpha -1} z'(t)+ \int_a^b q(t,\xi)f(x(g(t,\phi)))d\sigma (\xi) =0,\quad t\gt t_0,$$ where $\alpha \gt 0$ and $z(t)= x(t)+p(t)x(t-\tau)$. Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results

Sufficient conditions for oscillation of fourth-order neutral differential equations with distributed deviating arguments

Some new sufficient conditions are established for the oscillation of fourth-order neutral differential equations with continuously distributed delay. An example is provided to show the importance of these resul

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

Oscillation criteria of second order neutral delay dynamic equations with distributed deviating arguments

In this paper we establish some oscillation theorems for second order neutral dynamic equations with distributed deviating arguments. We use the Riccati transformation technique to obtain sufficient conditions for the oscillation of all solutions. Further, some examples are provided to illustrate the results

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

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