Oscillation of self-adjointmatrix differential systems

Oscillation Results for Second Order Self-adjoint Matrix Differential Systems

on [0,∞), where Y (t), P (t) and Q(t) are n × n real continuous matrix functions on [0,∞) with P (t), Q(t) symmetric and P (t) positive definite for t ∈ [0,∞) (P (t) > 0, t ≥ 0). A solution Y (t) of (1.1) is said to be nontrivial if det Y (t) 6= 0 for at least one t ∈ [0,∞) and a nontrivial solution Y (t) of (1.1) is said to be prepared (selfconjugated) if Y ∗(t)P (t)Y ′(t)− Y ∗′(t)P (t)Y (t) ≡...

Oscillation of the systems of impulsive hyperbolic partial differential equations

The systems of impulsive hyperbolic partial differential equations with Robin boundary value condition are investigated. Several new sufficient conditions of oscillation for such systems are established by employing impulsive differential inequalities and integration.

Oscillation of Nonlinear Systems of Matrix Differential Equations

For systems of matrix equations of the form £/' = A(t, U, V)V, V = -B(t,U,V) it is shown here that the oscillation problem can be reduced to the corresponding problem of "associated" (in some sense) scalar equations for which there exist numerous results. Furthermore, it is also shown that many of the existing results concerning the equation (A(t)U')' + B(t,U, U')U = 0 can be considerably impro...

Oscillation theorems for systems of linear differential equations

On systems of differential equations with extrinsic oscillation

We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subjected to highly oscillatory perturbations. This method is superior to standard ODE numerical solvers in the presence of high frequency forcing terms, and is based on asymptotic expansions of the solution in inverse powers of the oscillatory parameter ω, featuring modulated Fourier se...