Opuscula Math. 38, no. 3 (2018), 327-356
https://doi.org/10.7494/OpMath.2018.38.3.327

Opuscula Mathematica

# Improved iterative oscillation tests for first-order deviating differential equations

George E. Chatzarakis

Abstract. In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing $$\lim \sup$$ and $$\lim \inf$$ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.

Keywords: differential equation, non-monotone argument, oscillatory solution, nonoscillatory solution.

Mathematics Subject Classification: 34K06, 34K11.

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