We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2×2×2 hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this ...

We compare some recent results on bounded solutions (over Z) of nonlinear difference equations and systems to corresponding ones for nonlinear differential equations. Bounded input-bounded output problems, lower and upper solutions, Landesman-Lazer conditions and guiding functions techniques are considered.

Classification schemes for nonoscillatory solutions of nonlinear difference equations are important since further investigations of some of the qualitative behaviors of nonoscillatory solutions can then be reduced to only a number of cases. There are several studies which provide such classification schemes for difference equations, see, for example, [4– 11]. In particular, in [7], a class of n...

This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in...

Introduction: Multiple Sclerosis (MS) is a disease of central nervous system that mainly causes lesions or plaques in the spinal cord and brain. The purpose of this study was to analyze the relation between c.-813C>T (rs2070744) and c.894G>T (rs1799983) polymorphisms of NOS3 gene and MS in Iranian patients. Methods: A total of 78 patients with MS and 80 healthy controls were screened for NOS3 ...

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking, their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can o...

This paper is concerned with the nonlinear functional difference equation ∆x(n) = −a(n)x(n) + λh(n)f(n, x(n− τ(n))), where h and f may change sign. Sufficient conditions for the existence of at least one positive T−periodic solution are established.

We study weighted pseudo almost automorphic solutions for the nonlinear fractional difference equation ∆u(n) = Au(n+ 1) + f(n, u(n)), n ∈ Z, for 0 < α ≤ 1, whereA is the generator of an α-resolvent sequence {Sα(n)}n∈N0 in B(X). We prove the existence and uniqueness of a weighted pseudo almost automorphic solution assuming that f(·, ·) is weighted almost automorphic in the first variable and sat...

In this paper, we consider the higher order neutral nonlinear difference equation ∆(x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n)))− f2(n, x(σ2(n))) = 0, ∆(x(n) + p(n)x(τ(n))) + f1(n, x(σ1(n)))− f2(n, x(σ2(n))) = g(n), ∆(x(n) + p(n)x(τ(n))) + l X i=1 bi(n)x(σi(n)) = 0. We obtain sufficient conditions for the existence of non-oscillatory solutions.

This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f(t, u, v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem a...