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Oscillation criteria for third order nonlinear delay differential equations with damping

100%

Grace S. R.

Opuscula Mathematica

2015

tom Vol. 35, no. 4

485--497

This note is concerned with the oscillation of third order nonlinear delay differential equations of the form (r2(t) (r1(t)y'(t))')' +p(t)y'(t) + q(t)ƒ(y(g(t))) = 0. (*) In the papers [A.Tiryaki, M.F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007), 54-68] and [M.F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear-functional differential equations, Applied Math. Letters 23 (2010), 756-762], the authors established some sufficient conditions which insure that any solution of equation (*) oscillates or converges to zero, provided that the second order equation (r2(t)z'(t))' + (p(t)/r1(t))z(t) =0 (**) is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (*) oscillates if equation (**) is nonoscillatory. We also establish results for the oscillation of equation (*) when equation (**) is oscillatory.

Oscillation criteria of comparison type for second order deifference equations

63%

Grace S. R. , El-Morshedy H. A.

2000

tom Vol. 6, nr 1

87-103

In this paper we investigate the oscillatory character of the second order nonlinear difference equations of the forms (wzór) n = 1,2, ... and the corresponding nonhomogeneous equation (wzór) n= 1,2,... via comparison with certain second order linear difference equations where the function f is not necessarily monotonic. The results of this paper are essentially new and can be extended to more general equations.

Oscillation criteria for third order nonlinear difference equations

51%

Grace S. R. , Agarwal R. P. , Aktas M. F.

tom Nr 42

39-51

We shall establish some new criteria for the oscillation of third order nonlinear difference equations of the form ...[wzór]