On oscillations of solutions of second-order linear differential equations with constant complex coefficients

Abstract

By using a general result connected to the zeros of the solutions of linear ordinary differential equations with constant complex coefficients, we describe criteria for the existence of oscillatory and non-oscillatory solutions to the Cauchy problem for a second order linear homogeneous differential equation with constant complex coefficients. We deduce that the oscillatory behavior of the solutions does not depend on the initial conditions.

Keywords: Second order linear ordinary differential equation, oscillatory and non-oscillatory solutions, Cauchy problem, constant complex coefficients, characteristic roots.