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 $$f(t)\equiv g(t)\equiv 0.$$

MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems
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References:

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