with y−s, y−s+1, . . . , y−1 ∈ (0,∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = k+m. We prove that if gcd(2k,m) = 1, then solutions to this equation are asymptotically 2k-periodic. This generalizes the corresponding result for m = 3 and k = 1, proved in K. S. Berenhaut et al., Periodic Solutions of the Rational Difference Equation yn = yn−3+yn−4 yn−1 ,Journal of Difference Equations and Applicat...

In this note we consider the following high-order rational difference equation xn = 1+ k ∏ i=1 (1− xn−i ) k ∑ i=1 xn−i , n = 0, 1, . . . , where k ≥ 3 is odd number, x−k , x−k+1, x−k+2, . . . , x−1 is positive numbers. We obtain the boundedness of positive solutions for the above equation, and with the perturbation of initial values, we mainly use the transformation method to prove that the pos...

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

l~(t) = r(t)N(t) a bkN(hk(t)) cz(t)N(gl(t)), t >_ O, l = l N(t )=~( t ) , t<O, N(O)=No, is considered. The existence and the bounds of positive solutions are studied. Sufficient conditions for the extinction of the solution are presented. © 2005 Elsevier Ltd. All rights reserved. K e y w o r d s D e l a y logistic equations, Linear harvesting, Positive solutions, Extinction of the population, S...

In this article we prove the endogeny and bivariate uniqueness property for a particular “max-type” recursive distributional equation (RDE). The RDE we consider is the so called logistic RDE, which appears in the proof of the ζ(2)-limit of the random assignment problem using the local weak convergence method proved by D. Aldous [Probab. Theory Related Fields 93 (1992)(4), 507 – 534]. This artic...

Oscillation properties of solutions of the forced second order linear difference equation ∆(rk∆xk) + ckxk+1 = hk are investigated. The authors show that if the forcing term h does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-lin...

We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose-Einstein condensates. In this c...

We argue that Ulam-Hyers stability concept is quite significant in realistic problems in numerical analysis, biology and economics. A generalization to nonlinear systems is proposed and applied to the logistic equation (both differential and difference), SIS epidemic model, Cournot model in economics and a reaction diffusion equation. To the best of our knowledge this is the first time Ulam-Hye...