Oscillation and non-oscillation criteria for linear nonhomogeneous systems of two first-order ordinary differential equations. (English) Zbl 07428676

The paper delas with the linear system \begin{align*} \phi'&=p(t)\phi+q(t)\psi+f(t)\\ \psi'&=r(t)\phi+s(t)\psi+g(t),\tag{1} \end{align*}were all the 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 Riccati equation the auhtor 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 \(f(t)\equiv g(t)\equiv 0.\)


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34A30 Linear ordinary differential equations and systems
Full Text: DOI arXiv


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