Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

This paper is concerned with the existence of multiple periodic solutions for discrete Nicholson’s blowflies type system. By using the Leggett-Williams fixed point theorem, we obtain the existence of three nonnegative periodic solutions for discrete Nicholson’s blowflies type system. In order to show that, we first establish the existence of three nonnegative periodic solutions for the n-dimensional functional difference system yk+1=Akyk+fk, yk-τ, k∈ℤ, where Ak is not assumed to be diagonal as in some earlier results. In addition, a concrete example is also given to illustrate our results

Oscillation criterion for first-order linear differential equations with several delay arguments

By using iterated estimates involving all delay arguments, we establish an oscillation criterion for first-order linear differential equations with several delay arguments. This criterion is focused on the interaction among the delay arguments, instead of converting the original equation into a single delay equation and using existing results. Several examples illustrate the results obtained. Keywords: Differential equation, Oscillation, Multiple delay arguments, Mathematics Subject Classification: 34k11, 34C1

Oscillation of solutions to non-linear difference equations with several advanced arguments

This work concerns the oscillation and asymptotic properties of solutions to the non-linear difference equation with advanced arguments $$x_{n+1}- x_n =\sum_{i=1}^m f_{i,n}( x_{n+h_{i,n}}).$$ We establish sufficient conditions for the existence of positive, and negative solutions. Then we obtain conditions for solutions to be bounded, convergent to positive infinity and to negative infinity and to zero. Also we obtain conditions for all solutions to be oscillatory

Oscillations of nonlinear difference equations with deviating arguments

summary:This paper is concerned with the oscillatory behavior of first-order nonlinear difference equations with variable deviating arguments. The corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given