Oscillation of nonlinear hyperbolic equations with distributed deviating arguments

Oscillations of solutions to nonlinear hyperbolic equations with continuous distributed deviating arguments are studied. By employing some integral means of solutions, the multi-dimensional oscillation problems are reduced to one-dimensional oscillation problems

Numerical test for hyperbolicity of chaotic dynamics in time-delay systems

We develop a numerical test of hyperbolicity of chaotic dynamics in time-delay systems. The test is based on the angle criterion and includes computation of angle distributions between expanding, contracting and neutral manifolds of trajectories on the attractor. Three examples are tested. For two of them previously predicted hyperbolicity is confirmed. The third one provides an example of a time-delay system with nonhyperbolic chaos.Comment: 7 pages, 5 figure

Oscillations of Hyperbolic Systems with Functional Arguments

Hyperbolic systems with functional arguments are studied, and sufficient conditions are obtained for every solution of boundary value problems to be weakly oscillatory (that is, at least one of its components is oscillatory) in a cylindrical domain. Robin-type boundary condition is considered. The approach used is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems by using some integral means of solutions

Oscillations of vector differential equations of hyperbolic type with functional arguments

Vector hyperbolic differential equations with functional arguments are studied, and oscillations of solutions of certain boundary value problems are investigated. The approach used is to reduce the multi-dimensional oscillation problems to the nonexistence of positive solutions of scalar functional differential inequalities by employing the concept of H-oscillation introduced by Domšlak, where H denotes some unit vector

Oscillation Properties for Systems of Hyperbolic Differential Equations of Neutral Type

AbstractSufficient conditions are established for the oscillations of systems of hyperbolic differential equations of the form∂2∂t2ptuix,t+∑r=1dλrtuix,t−τr =aitΔuix,t+∑j=1m∑k=1saijktΔujx,ρkt −qix,tuix,t−∑j=1m∑h=1lqijhx,tujx,σht, x,t∈Ω×0,∞≡G,i=1,2,…,m,where Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space Rn

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

Oscillation properties for parabolic equations of neutral type

summary:The oscillation of the solutions of linear parabolic differential equations with deviating arguments are studied and sufficient conditions that all solutions of boundary value problems are oscillatory in a cylindrical domain are given