6,211 research outputs found
Oscillation theorems for second order neutral differential equations
In this paper new oscillation criteria for the second order neutral differential equations of the form
\begin{equation*}
\left(r(t)\left[x(t)+p(t)x(\tau(t))\right]'\right)'+q(t)x(\sigma(t))+v(t)x(\eta(t))=0
\tag{}\end{equation*}
are presented. Gained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the second order equation to the oscillation of the first order equation. Obtained comparison principles essentially simplify the examination of the studied equations. We cover all possible cases when arguments are delayed, advanced or mixed
Sharp results for oscillation of second-order neutral delay differential equations
The aim of the present paper is to continue earlier works by the authors on the oscillation problem of second-order half-linear neutral delay differential equations. By revising the set method, we present new oscillation criteria which essentially improve a number of related ones from the literature. A couple of examples illustrate the value of the results obtained
Necessary and sufficient conditions for oscillation of second-order differential equations with nonpositive neutral coefficients
summary:In this work, we present necessary and sufficient conditions for oscillation of all solutions of a second-order functional differential equation of type where . Under the assumption , we consider two cases when and . Our main tool is Lebesgue's dominated convergence theorem. Finally, we provide examples illustrating our results and state an open problem
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
On the oscillation of third-order quasi-linear neutral functional differential equations
summary:The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation
\begin{equation*} \big [a(t)\big ([x(t)+p(t)x(\delta (t))]^{\prime \prime }\big )^\alpha \big ]^{\prime }+q(t)x^\alpha (\tau (t))=0\,, E \end{equation*}
where , and . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results
Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations
We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature
Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations
New oscillation criteria are established for the second-order nonlinear neutral
functional differential equations of the form (r(t)|z′(t)|α−1z′(t))’+f(t,x[σ(t)])=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), p∈C1([t0,∞),[0,∞)), and α≥1. Our results improve and
extend some known results in the literature. Some examples are also provided to show the
importance of these results
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