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Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation

Graef J. R., Tunc E., Grace S. R.

Opuscula Mathematica

2017

Vol. 37, no. 6

839--852

This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.

Boundedness of solutions of nonlinear three-dimensional difference systems with delays

Schmeidel E.

Fasciculi Mathematici

2010

Nr 44

107-113

In this paper three-dimensional nonlinear difference system with delays ...[wzór] is investigated. The classification of nonoscillatory solutions of the considered system are presented. Next, the sufficient conditions under which nonoscillatory solution of considered system is bounded or is unbounded are given. Key words: difference equation, nonlinear system, nonoscillatory, bounded, unbounded solution.