In this paper, some properties of all positive solutions are considered for a higher order rational difference equation, mainly for the existence of eventual prime period two solutions, the existence and asymptotic behavior of nonoscillatory solutions and the global asymptotic stability of its equilibria. Our results show that a positive equilibrium point of this equation is a global attractor ...

For any integer m let P (m) denote the greatest prime factor of m and let Q(m) denote the greatest square free factor of m with the convention that P (0) = P (±1) = 1 = Q(±1) = Q(0). Thus, if m = p1 1 · · · p hr r with p1, . . . , pr distinct primes and h1, . . . , hr positive integers, then Q(m) = p1 · · · pr. van der Poorten and Schlickewei [6] and Evertse [1] proved, by means of a p-adic ver...

Let G be the space of generating functions of a periodic infinite order linear recurrence. In this paper we provide an explicit procedure for computing a basis of G. AMS Subject Classifications: 15A15, 39A06, 92D25,39A06.

This paper deals with obtaing necessary and sufficient conditions for the existence of at least one Ψ-bounded solution for the non-homogeneous matrix difference equation X(n+1) = A(n)X(n)B(n)+F (n), where F (n) is a Ψ-bounded matrix valued function on Z+. Finally, we prove a result relating to the asymptotic behavior of the Ψ-bounded solutions of this equation on Z+.

We deene an innnite array A of nonnegative integers based on a linear recurrence, whose second row provides basis elements of an exotic ternary numeration system. Using the numeration system we explore many properties of A. Further, we propose and analyze a family Frankenstein of 2-player pebbling games played on a semi-innnite strip, and present a winning strategy based on certain subarrays of...

A family of sequences produced by a non-homogeneous linear recurrence formula derived from the geometry of circles inscribed in lenses is introduced and studied. Mysterious “underground” sequences underlying them are discovered in this paper.

Using a fixed point theorem of strict-set-contraction, we some established the existence of positive periodic solutions for the neutral logistic difference equation, with multiple delays, ∆x(n) = x(n) h a(n)− p X i=1 ai(n)x(n− τi(n))− q X j=1 cj(n)∆x(n− σj(n)) i .

A previous paper,1 denoted by I, reported observation of universal chaotic behavior for a driven nonlinear semiconductor oscillator which shows successive period-doubling bifurcations as a route to chaos.2 Semiquantitative agreement was observed for several universal numbers computed from simple nonlinear finite difference equations of the Feigenbaum universality class, which includes the logis...

We prove the existence and uniqueness of a positive solution to a logistic system of differential difference equations that arises as a population model for a single species which is composed of several habitats connected by linear migration rates. Our proof is based on the proof of a similar result for a reaction-advection-diffusion equation.