Sufficient Conditions for Oscillation of Linear Second Order Matrix Differential Systems

Abstract

Sufficient conditions in terms of trace are obtained for the oscillation of all nontrivial prepared solutions of second order self-adjoint differential matrix systems (P(t)Y')' + Q(t)Y = 0, t ≥ σ ≥ 0, where P and Q are n x n real continuous symmetric matrix functions on [σ,∞) with P(t) positive definite. Our results generalize earlier results on oscillation of scalar second order equation (p(t)y')' + q(t)y = 0, t ≥ σ ≥ 0, where p,q ∈ C([σ,∞),(-∞,∞)) with p(t) > 0, and are applicable to Euler's second order matrix equations.