The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables reduction of linearization problem to a system of first order partial differential equations. By means of inverse of the Poincaré map one can relate symmetries in ...

We consider the asymptotic behavior of bounded solutions of the difference equations of the form x(n + 1) = Bx(n) + y(n) in a Banach space X, where n = 1, 2, ..., B is a linear continuous operator in X, and (y(n)) is a sequence in X converging to 0 as n → ∞. An obtained result with an elementary proof says that if σ(B) ∩ {|z| = 1} ⊂ {1}, then every bounded solution x(n) has the property that li...

In this paper, a fourth-order nonlinear p-Laplacian difference equation is considered. Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. The existing results are generalized and significantly complemented.

By using the critical point theory, we establish some existence criteria to guarantee that the nonlinear difference equation ΔΔpnΔxn − 1 δ − qnxn δ fn, xn has at least one homoclinic solution, where n ∈ Z, xn ∈ R, and f : Z × R → R is non periodic in n. Our conditions on the nonlinear term fn, xn are rather relaxed, and we generalize some existing results in the literature.

In this article, we study a higher-order nonlinear difference equation. By using critical point theory, we establish sufficient conditions for the existence of periodic solutions.

We consider a class of fourth-order nonlinear difference equations. The classification of nonoscillatory solutions is given. Next, we divide the set of solutions of these equations into two types: F+and F−-solutions. Relations between these types of solutions and their nonoscillatory behavior are obtained. Necessary and sufficient conditions are obtained for the difference equation to admit the...

The main result is an improvement of previous results on the equation f(x) + f(y)− f(x+ y) = g[φ(x) + φ(y)− φ(x+ y)] for a given function φ. We find its general solution assuming only continuous differentiability and local nonlinearity of φ. We also provide new results about the more general equation f(x) + f(y)− f(x+ y) = g(H(x, y)) for a given function H. Previous uniqueness results required ...

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applic...

We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x„+l = x„f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x„er^~x"-k'1 .

In this paper, we present a generalization of the relational data model based on interval neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle incomplete information. Associated with each relation are two membership functions one is called truth-membership function T which ...