By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

γδ T cells constitute a sizeable and non-redundant fraction of the total T cell pool in all jawed vertebrates, but in contrast to conventional αβ T cells they are not restricted by classical MHC molecules. Progress in our understanding of the role of γδ T cells in the immune system has been hampered, and is being hampered, by the considerable lack of knowledge regarding the antigens γδ T cells ...

We present, for the first time, two hierarchies of nonlinear, integrable q-difference equations, one of which includes a q-difference form of each of the second and fifth Painlevé equations, qPII and qPV, the other includes qPIII. All the equations have multiple free parameters. A method to calculate a 2× 2 Lax pair for each equation in the hierarchy is also given.

Asymptotic properties of some non-linear difference equations are considered. AMS(1980) Subject Classification: 39A12, 45E99..

One of the earliest difference equations, the Fibonacci sequence, was introduced in 1202 in “Liberabaci,” a book about the abacus, by the famous Italian Leonardo di Pisa, better known as Fibonacci. The problem may be stated as follows: how many pairs of rabbits will there be after one year when starting with one pair of mature rabbits, if each pair of rabbits give birth to a new pair each month...

The boundedness character of positive solutions of two nonlinear fourth-order difference equations, which are particular cases of two large classes of difference equations by Stević, are studied in this paper.

In this paper, we consider the nonlinear difference equation xn 1 f xn−l 1, xn−2k 1 , n 0, 1, . . . , where k, l ∈ {1, 2, . . . } with 2k / l and gcd 2k, l 1 and the initial values x−α, x−α 1, . . . , x0 ∈ 0, ∞ with α max{l − 1, 2k − 1}. We give sufficient conditions under which every positive solution of this equation converges to a not necessarily prime 2-periodic solution, which extends and ...