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Oscillations in systems of impulsive nonlinear partial differential equations with distributed deviating arguments

Bortolan M. C., Chatzarakis G. E., Kalaimani T., Raja T., Sadhasivam V.

Fasciculi Mathematici

2019

nr 62

13--33

In this paper, we consider systems of impulsive nonlinear neutral delay partial differential equations with distributed deviating arguments and sufficient conditions for the oscillation of the system under the Dirichlet boundary condition. The main results are illustrated by one example.

Improved iterative oscillation tests for first-order deviating differential equations

Chatzarakis G. E, Jadlovska I.

Opuscula Mathematica

2018

Vol. 38, no. 3

327--356

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.