New oscillation criteria for first order neutral delay difference equations Selvaraj B.1, Jawahar G. Gomathi2 1Dean, Department of Science and Humanities, Nehru Institute of Engineering and Technology, Coimbatore-641105 Email: Professorselvaraj@rediffmail.com 2Department of Mathematics, Karunya University, Coimbatore-641114 Email: jawahargomathi@yahoo.com 2000 Mathematics subject classification: 39A10 Online published on 22 February, 2013. Abstract In this paper we deal with the oscillatory criteria for all solutions of first order neutral delay difference equation with positive and negative coefficients. Here we consider the neutral delay difference equation of the form,
 | ( 1.1 ) |
where nεN(n0), n0 is a nonnegative integer and Δ is the forward difference operator. Here we assume {Pn}, {qn} are positive sequences and {rn} is a real sequence. f and g are continuous functions such that uf(u) ≠ 0, and ug(u) ≠0, for u ≠ 0. Also k,l,m are positive integers. Here Δ is the forward difference operator defined by ΔYn= Yn+l-Yn. By a solution of (1.1) we mean a real sequence {xn} which satisfies the equation(1.1) for all nεN0. A solution {xn} of (1.1) is said to be oscillatory if the terms of the sequence are not eventually positive, or not eventually negative. Otherwise it is called nonoscillatory. Equation (1.1) is said to be oscillatory if all its solutions are oscillatory. Following this trend, in this paper we find some sufficient conditions for oscillation of all solutions of equation(1.1). Top Keywords oscillation, neutral, difference equations. Top |