monotone method for equations describing transport phenomena in a banach space in this paper monotone methods have been developed for equations arising in transport processes in a banach space this method proves the existence of extremal solutions for such equations the advantage of the method for such type of equations is that the successive iterates are solutions of the corresponding initial value problems

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 sturm liouville type boundary value problem abstract the problems of existence uniqueness and continuous dependence on parameter of solutions of the nonlinear boundary value problem of sturm liouville type for ordinary differential equations are considered the well known banach fixed point theorem is used to establish results

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

application of difference equations in divisibility abstract we present an easy applicable method which for a large class of integer sequences a n shows when all their terms are divisible by a natural number m 1

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

on some systems of difference equations abstract in this note we show that the following systems of difference equations u n 1 v n 1 v n v n 1 u n 1 u n u n 1 v n 1 u n v n 1 u n 1 v n u n 1 u n 1 v n v n 1 v n 1 u n with n n 0 and complex initial values u 0 and v 0 are solvable explicitly by means of riccati equations and based on the formulae for the general solutions we present the behaviour of their solutions as n while the result is natural for the first system it is a bit surprising for the other two systems

on the difference equation xn xn 2 bn cnxn 1xn 2 abstract we prove that the difference equation x n x n 2 b n c n x n 1 x n 2 n n 0 where b n n n 0 and c n n n 0 are sequences periodic with period two and the initial values x 2 x 1 are real numbers can be solved explicitly some applications of obtained formulae are given

global stability of a difference equation with maximum we prove that every positive solution to the difference equationx n maxa 1x n 1 a 1 a 2x n 2 a 2 a kx n k a k email protected n 0 where email protected n a i 0 a email protected 0 1 i 1 k converges to the following quantity maxa 1 1 a 1 1 a k 1 a k 1 confirming a quite recent conjecture of interest we also prove another result on global convergence which concerns some cases when not all a i i 1 k belong to the interval 0 1

boundedness character of a class of difference equations abstract a complete picture regarding the boundedness character of positive solutions to the following difference equation x n max a x n 1 p x n k p n n 0 where k 2 and the parameters a and p are positive real numbers is given in particular for the case p k 1 0 k k k 1 k 1 we prove that all solutions to the equation are bounded we also present corresponding results concerning the following closely related difference equation x n a x n 1 p x n k p n n 0

on discrete boundary value problems arising in transport phenomena for the discrete boundary value problems arising in transport processes we provide comparison results these results are used to develop monotone iterative methods for the construction of the maximal and minimal solutions in a sector the advantage of this technique is that the successive approximations are the solutions of the initial and terminal value problems numerical illustration showing the sharpness as well the importance of the obtained results is also included

on a system of difference equations with maximum in this paper we study the periodic character of the solutions of the system of difference equations with maximum x n 1 max a y n x n 1 y n 1 max b x n y n 1 where a b are positive constants and the initial values x 1 x 0 y 1 y 0 are positive numbers we prove that every solution is eventually periodic

on a difference equation with maximum abstract this paper studies the asymptotic behavior of positive solutions to the difference equation x n max 1 x n 1 a x n 2 n 0 1 where 0 0 we prove that every positive solution of this equation approaches x 1 or is eventually periodic with period 4 according as a 1 or a 1

on a solvable rational system of difference equations abstract we show that the system of difference equations x n 1 x n y n k y n k 1 a n b n x n y n k y n 1 y n x n k x n k 1 c n d n y n x n k n n 0 where k n the sequences a n b n c n d n n n 0 and initial values x i y i i 0 k are real numbers can be solved in closed form by using obtained formulae we investigate asymptotic behavior of well defined solutions of the system for the case when all the sequences a n b n c n and d n are constant

on the system of difference equations xn cnyn 3 an bnyn 1xn 2y n 3 yn γnxn 3 αn βnxn 1yn 2 xn 3 we show that the system of difference equationsx n c ny n 3a n b ny n 1x n 2y n 3 y email protected nx n email protected email protected nx n 1y n 2x n 3 email protected n 0 where the sequences 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 3 are real numbers such that c n 0 c n 0 email protected n 0 can be solved in closed form and for the case when all the sequences a n b n c n a n b n and c n are constant we describe the asymptotic behavior of well defined solutions of the system

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

global stability of a max type difference equation we show that every positive solution to the difference equationx n maxa 1x n p 1 a 1 a 2x n p 2 a 2 a kx n p k a k n n 0 where p i i 1 k are natural numbers such that 1 0 a i 1 1 i 1 k converges to max 1 i ka i 1 a i 1 this result improves and complements the main result in our recent note s stevic global stability of a difference equation with maximum appl math comput 210 2009 525 529 since it also considers the case when a i 1 0 i 1 k

a sequential procedure for multihypothesis testing the sequential testing of more than two hypotheses has important applications in direct sequence spread spectrum signal acquisition multiple resolution element radar and other areas a useful sequential test which we term the msprt is studied in this paper the test is shown to be a generalization of the sequential probability ratio test under bayesian assumptions it is argued that the msprt approximates the much more complicated optimal test when error probabilities are small and expected stopping times are large bounds on error probabilities are derived and asymptotic expressions for the stopping time and error probabilities are given a design procedure is presented for determining the parameters of the msprt two examples involving gaussian densities are included and comparisons are made between simulation results and asymptotic expressions comparisons with bayesian fixed sample size tests are also made and it is found that the msprt requires two to three times fewer samples on average

on the max type equation xn 1 max axn xn 2 abstract we show that every well defined solution of the difference equation x n 1 max a x n x n 2 n n 0 where a r is eventually periodic with period three

monotone method for nonlinear boundary value problems arising in transport processes recently monotone iterative methods have been successfully employed to prove existence of multiple solutions and point wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations because of the importance of this problem in other physical applications we extend in this paper the monotone technique to a general class of nonlinear boundary value problem which includes the transport problem treated as a special case