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Oscillations of fourth order quasilinear difference equations

100%

Thandapani E. , Selvaraj B.

Fasciculi Mathematici

2007

tom Nr 37

109-119

Consider the fourth order quasilinear difference equation of the form where {pn} is a positive sequence and {qn} is a sequence of non-negative reals, a and ,3 are ratios of odd positive integers. We obtain some new sufficient conditions for the oscillation of all solutions of equation (*). Examples are inserted to illustrate the importance of our results.

Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

80%

Thandapani E. , Selvarangam S. , Rama R. , Madhan M.

tom Nr 56

155--165

In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form ∆(an (∆zn )α )+qn f(xn-σ) )=0, n>no >0, where zn - xn - pn xn-r, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

Oscillation criteria for even order neutral difference equations

80%

Selvarangam S. , Rupadevi S. A. , Thandapani E. , Pinelas S.

tom Vol. 39, no. 1

91--108

In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form [formula] where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results.