Oscillation and non-oscillation criteria for linear nonhomogeneous systems of two first-order ordinary differential equations (Q2247709)

The paper deals with the linear system \[ \begin{aligned} \phi'&=p(t)\phi+q(t)\psi+f(t)\\ \psi'&=r(t)\phi+s(t)\psi+g(t), \end{aligned}\tag{1} \] where all functions are supposed to be continuous functions and also a special case of this system written in the form of the second order differential equation \[ (a(t)\phi')'+b(t)\phi'+c(t)\phi=d(t).\tag{2} \] Using the transformation into a Riccati equation the author derives oscillation and nonoscillation criteria for these equations. These criteria are based on a comparison of the system (1) with the homogeneous system obtained from (1) by letting \(f(t)\equiv g(t)\equiv 0.\)