We determine a decomposition of the solution fractional difference initial-value problem with periodic right-hand side. For problems S-asymptotically N-periodic side, sufficient condition is proved for existence an solution.

A numerical method is proposed for computing time-periodic and relative time-periodic solutions in dissipative wave systems. In such solutions, the temporal period, and possibly other additional internal parameters such as the propagation constant, are unknown priori and need to be determined along with the solution itself. The main idea of the method is to first express those unknown parameter...

and Applied Analysis 3 Proof. We can write terms of a period-three solution of 1.1 as x−1 a, x0 b, x1 ab − 1, x2 b ab − 1 − 1 a ⇐⇒ ab2 − b − 1 a ⇐⇒ ab2 a b 1, x3 a ab − 1 − 1 b ⇐⇒ a2b − a − 1 b ⇐⇒ a2b a b 1. 2.4 Therefore, this is indeed a solution of period three if the system below is satisfied. ab2 a b 1, a2b a b 1. 2.5 Hence we see that ab2 a2b. Thus, this is true if a 0, or if b 0, or if a...

We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in nu...

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As we know, the coefficients of impulsive Lasota-Wazewska model are always assumed to be continuous, say, periodic and almost periodic. In this paper we consider the case when the coefficients are piecewise almost periodic, and establish an existence and uniqueness theorem of piecewise almost periodic positive solution for this model. Mathematics Subject Classifications: 34C27, 34A37

In this paper, we study the existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems. By using the method of coincidence degree and Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution of periodic n-species Lotka-Volt...

We use the concept of the Filippov solution to study the dynamics of a class of delayed dynamical systems with discontinuous right-hand side, which contains the widely studied delayed neural network models with almost periodic self-inhibitions, interconnection weights, and external inputs. We prove that diagonal-dominant conditions can guarantee the existence and uniqueness of an almost periodi...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...