Existence of positive solutions for nth-order periodic difference equations

This paper is devoted to the study of difference equations coupled with periodic boundary value conditions. We deduce the existence of at least one positive solution provided that the nonlinear part of the equation satisfies some monotonicity assumptions and the existence of a positive upper solution. The result is obtained from a new fixed point theorem based on the classical Krasnoselskii's cone expansion/contraction theorem and the constant sign properties of the related Green's function.     

Existence of periodic and subharmonic solutions for second order functional difference equations

In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.     

一类差分系统周期解的存在性

This paper studies the nonautonomous nonlinear system of difference equations △x(n) = A(n)x(n) f(n, x(n)), n ∈ Z, (*)where x(n) ∈ RN,A(n) = (aij(n))N×N is an N × N matrix, with aij∈ C(R,R) for i,j =ω, z) = f(t, z) for any t ∈ R, (t, z) ∈ R × RN and ω is a positive integer. Sufficient conditions for the existence of ω-periodic solutions to equations (*) are obtained.     

Existence of periodic solutions

An apparatus for proving existence theorems for periodic solutions of equations with discontinuous right-hand side and differential inclusions is developed. Translated fromMatematischeskie Zametki, Vol. 61, No. 5, pp. 769–784, May, 1997. Translated by V. N. Dubrovsky     

Periodicity and solutions of some rational difference equations systems

In this paper we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case. Moreover, we study the periodicity of solutions for such systems. Finally, some numerical examples are presented.     

Asymptotically almost periodic solutions of nonlinear Volterra difference equations with unbounded delay

The existence of almost periodic solutions of nonlinear Volterra difference equations with unbounded delay is obtained by using uniform stability properties of a bounded solution. An example is also given to illustrate obtained results.     

Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

Existence and asymptotic behaviour of solutions to first- and second-order difference equations with periodic forcing

By using previous results of Djafari Rouhani for non-expansive sequences in Refs (Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale University, Part I (1981), pp. 1–76; Djafari Rouhani, J. Math. Anal. Appl. 147 (1990), pp. 465–476; Djafari Rouhani, J. Math. Anal. Appl. 151 (1990), pp. 226–235), we study the existence and asymptotic behaviour of solutions to first-order as well as second-order difference equations of monotone type with periodic forcing. In the first-order case, our result extends to general maximal monotone operators, the discrete analogue of a result of Baillon and Haraux (Rat. Mech. Anal. 67 (1977), 101–109) proved for subdifferential operators. In the second-order case, our results extend among other things, previous results of Apreutesei (J. Math. Anal. Appl. 288 (2003), 833–851) to the non-homogeneous case, and show the asymptotic convergence of every bounded solution to a periodic solution.     

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations△2xn-1+f(n,xn)=0some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinityin z.     

Almost periodic homogeneous linear difference systems without almost periodic solutions

Almost periodic homogeneous linear difference systems are considered. It is supposed that the coefficient matrices belong to a group. The aim was to find such groups that the systems having no non-trivial almost periodic solution form a dense subset of the set of all considered systems. A closer examination of the used methods reveals that the problem can be treated in such a generality that the entries of coefficient matrices are allowed to belong to any complete metric field. The concepts of transformable and strongly transformable groups of matrices are introduced, and these concepts enable us to derive efficient conditions for determining what matrix groups have the required property.     

Existence of periodic solutions for nonlinear evolution equations with pseudo monotone operators

In this paper, we study the existence of -periodic solutions for the problem

where is a -periodic, pseudo monotone mapping from a reflexive Banach space into its dual.

     

Existence of time periodic solutions for the 3-D viscous primitive equations of large-scale dry atmosphere

In this paper, we consider the existence of time periodic solutions of the 3-D viscous primitive equations of large-scale dry atmosphere. We used the Galerkin method. Firstly, by Leray-Schauder fixed point theorem, we prove the existence of approximate solutions of the primitive equations, then we show the convergence of the approximate solutions, and we also get the uniqueness to the primitive equations.     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

Max‐type system of difference equations with positive two‐periodic sequences

This paper deals with the form and the periodicity of the solutions of the max‐type system of difference equations where , and are positive two‐periodic sequences and initial values x₀, x _{? 1}, y₀, y _{? 1} ∈ (0, + ∞ ). Copyright © 2014 John Wiley & Sons, Ltd.     

Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions.     

Existence of multiple positive periodic solutions for nonlinear functional difference equations

In this paper, we investigate the existence of multiple positive periodic solutions to a class of functional difference equations. We answer the open problems proposed by Y. Raffoul in [Electron. J. Differential Equations 55 (2002) 1-8] and the conditions obtained improve some recent results established there.     

Note on periodic solutions of fractional differential equations

The existence and nonexistence of periodic solutions are discussed for fractional differential equations by varying the lower limits of Caputo derivatives. The developed approach is illustrated on several examples.