on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

on the difference equation yn 1 α βe yn γ yn 1 in this paper we investigate the convergence the boundedness and the periodic character of the positive solutions of the difference equationy n email protected email protected y email protected y n 1 n 0 1 2 where the parameters a b c are positive numbers and the initial conditions y 1 y 0 are arbitrary non negative numbers

fixed point attractor analysis for a class of neurodynamics nearly all models in neural networks start from the assumption that the input output characteristic is a sigmoidal function on parameter space we present a systematic and feasible method for analyzing the whole spectrum of attractors all saturated all but one saturated all but twosaturated and so on of a neurodynamical system with a saturated sigmoidal function as its input output characteristic we present an argument that claims under a mild condition that only all saturated or all but one saturated attractors are observable for the neurodynamics for any given all saturated configuration all but one saturated configuration the article shows how to construct an exact parameter region r such that if and only if the parameters fall within r then is an attractor a fixed point of the dynamics the parameter region for an all saturated fixed point attractor is independent of the specific choice of a saturated sigmoidal function whereas for an all but one saturated fixed point it

on some linear difference equations and inequalities with continuous argument abstract we study some properties of solutions of linear difference equations and inequalities with continuous argument in terms of the location of the zeroes of the characteristic polynomial of the associated homogeneous linear difference equation with constant coefficients

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

long term behavior of positive solutions of a system of max type difference equations abstract some sufficient conditions which guaranty the attractivity of all positive solutions of the next system of difference equations x n max a y n 1 p j 2 k x n j q j y n max a x n 1 p j 2 k y n j q j n n 0 where a p 0 and q j j 2 k are nonnegative numbers are given the boundedness character of positive solutions of the system is also studied

on a system of difference equations of odd order solvable in closed form it is shown that the next system of difference equationsx n c ny n 2 k 1 a n b ny n 2 k 1 i 1 k 1y n 2 i 1 x n 2 i y email protected nx n 2 k 1 a email protected nx n 2 k 1 i 1 k 1x n 2 i 1 y n 2 email protected n 0 where a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 2k 1 are real numbers is solved in closed form and the behavior of its well defined solutions when all the coefficients in the system are constant is described

existence uniqueness and attractivity of prime period two solution for a difference equation of exponential form abstract in this paper we study the existence uniqueness and attractivity of prime period two solution of the difference equation x n 1 a bx n 1 e x n where a b are positive constants and the initial values x 1 x 0 are positive numbers

global stability and asymptotics of some classes of rational difference equations in this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable using a berg s result we also find asymptotics of some solutions of these equations

eventual periodicity of some systems of max type difference equations the periodicity of the next system of max type difference equations xn 1 max1 i1 m1f1i1xn ki1 1 1 1 xn ki1 2 1 2 xn ki1 l 1 l n xn t1s 1 xn 2 max1 i2 m2f2i2xn ki2 1 2 1 xn ki2 2 2 2 xn ki2 l 2 l n xn t2s 2 xn l max1 il mlflilxn kil 1 l 1 xn kil 2 l 2 xn kil l l l n xn tls l n n0n n0 where s l mj tj kij h j n j h 1 l j h 1 l 1 2 l 1 2 l is a permutation of 1 2 l 1 2 l and fjij 0 l n0 0 fjij 0 l n0 0 j 1 l j 1 l ij 1 mj ij 1 mj is studied it is shown that under some conditions posed on functions fjijfjij all positive solutions of the system are eventually periodic with period ts for some t nt n

study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form in this paper we study the boundedness the persistence and the asymptotic behavior of the positive solutions of the following systems of two difference equations of exponential form xn 1 a be yn c yn 1 y n 1 d e xn f xn 1

local existence of lipschitz continuous solutions of systems of nonlinear functional equations with iterated deviations abstract some conditions which guarantee the local existence of lipschitz continuous solutions of some systems of nonlinear functional equations with complicated deviations dependent of unknown functions are presented

a coupled system of rational difference equations abstract we investigate the global stability properties and asymptotic behavior of solutions of the recursive sequence where the parameters a b c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers

global asymptotic behavior of a two dimensional difference equation modelling competition we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 xn a cyn yn 1 yn b dxn n 0 1 where the parameters a and b are in 0 1 c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers we show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior in the case where a b we find an explicit equation for the stable manifold

eventually constant solutions of a rational difference equation we describe all the solutions of a rational difference equation from putnam s mathematical competition which are eventually equal to its positive equilibrium email protected 1 as a consequence we give a new elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one moreover we show that almost all solutions of the equation are not eventually equal to one

on a class of third order nonlinear difference equations this paper studies the boundedness character of the positive solutions of the difference equation x n 1 a x n px n 1 qx n 2 r n n 0 where the parameters a p q and r are positive numbers

difference equations and nonexistence of solutions of an integral equation abstract by using difference equations we give some easily applicable sufficient conditions for the non existence of nonnegative solutions satisfying some additional conditions of the integral equation f x x a x t b x t f t p d t where p 1 and x is a measurable space with probability measure

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

on the nonautonomous difference equation xn 1 an xn 1pxnq abstract in this paper we study the asymptotic behavior and the periodicity of the positive solutions of the nonautonomous difference equation x n 1 a n x n 1 p x n q n 0 1 where an is a positive bounded sequence p q 0 and x 1 x0 are positive numbers

oscillation and global asymptotic stability in a discrete epidemic model abstract in this paper we study the oscillation global asymptotic stability and other properties of the positive solutions of the difference equation x n 1 1 j 0 k 1 x n j 1 e ax n where a 0 k 2 3 and the initial values x k 1 x k 2 x0 are arbitrary real positive numbers such that j 0k 1x j

distributional and classical solutions to the cauchy boltzmann problem for soft potentials with integrable angular cross section this paper focuses on the study of existence and uniqueness of distributional and classical solutions to the cauchy boltzmann problem for the soft potential case assuming s n 1 integrability of the angular part of the collision kernel grad cut off assumption for this purpose we revisit the kaniel shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes the large data near local maxwellian regime with possibly infinite initial mass we study the propagation of regularity using a recent estimate for the positive collision operator given in alonso et al in convolution inequalities for the boltzmann collision operator arxiv 0902 0507 math ap by e carneiro and the authors that allows us to show such propagation without additional conditions on the collision kernel finally an l p stability result with 1 p is presented assuming the aforementioned condition

on a modification of a discrete epidemic model in this paper under some conditions on the constants a b 0 we study the existence of positive solutions the existence of a unique nonnegative equilibrium and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations x n 1 1 y n y n 1 1 e a y n y n 1 1 x n x n 1 1 e b x n where a b 0 and the initial values x 1 x 0 y 1 y 0 are positive numbers which satisfy the relations x 0 x 1 1 x 0 x 1 1 e b x 0 1 x 0 1 y 0 y 1 1 e a y 0