On Nonoscillation of Mixed Advanced-Delay Differential Equations with Positive and Negative Coefficients

For a mixed (advanced--delay) differential equation with variable delays and coefficients $$\dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0$$ where $$a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t$$ explicit nonoscillation conditions are obtained.Comment: 17 pages; 2 figures; to appear in Computers & Mathematics with Application

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{$E$}\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

Oscillation criteria for second order superlinear neutral delay differential equations

New oscillation criteria for the second order nonlinear neutral delay differential equation $[y(t)+p(t)y(t-\tau )]^{^{\prime \prime}}+q(t)\,f(y(g(t)))=0$, $t\geq t_{0}$ are given. The relevance of our theorems becomes clear due to a carefully selected example

Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument

The chapter is devoted to study the oscillation of all solutions to second‐order nonlinear neutral damped differential equations with delay argument. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and integral averaging techniques

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

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 $$(r(t)(z'(t))^\gamma )' +\sum _{i=1}^m q_i(t)x^{\alpha _i}(\sigma _i(t))=0, \quad t\geq t_0,$$ where $z(t)=x(t)+p(t)x(\tau (t))$. Under the assumption $\int ^{\infty }(r(\eta ))^{-1/\gamma } {\rm d}\eta =\infty$, we consider two cases when $\gamma >\alpha _i$ and $\gamma <\alpha _i$. Our main tool is Lebesgue's dominated convergence theorem. Finally, we provide examples illustrating our results and state an open problem