Displaying similar documents to “Existence and uniqueness of periodic solutions of mixed monotone functional differential equations.”

Systems of nonlinear delay integral equations modelling population growth in a periodic environment

Antonio Cañada, Abderrahim Zertiti (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we study the existence and uniqueness of positive and periodic solutions of nonlinear delay integral systems of the type x ( t ) = t - τ 1 t f ( s , x ( s ) , y ( s ) ) d s y ( t ) = t - τ 2 t g ( s , x ( s ) , y ( s ) ) d s which model population growth in a periodic environment when there is an interaction between two species. For the proofs, we develop an adequate method of sub-supersolutions which provides, in some cases, an iterative scheme converging to the solution.

Some boundedness results for systems of two rational difference equations

Gabriel Lugo, Frank Palladino (2010)

Open Mathematics

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We study k th order systems of two rational difference equations x n = α + i = 1 k β i x n - 1 + i = 1 k γ i y n - 1 A + j = 1 k B j x n - j + j = 1 k C j y n - j , y n = p + i = 1 k δ i x n - i + i = 1 k ε i y n - i q + j = 1 k D j x n - j + j = 1 k E j y n - j n . In particular, we assume non-negative parameters and non-negative initial conditions, such that the denominators are nonzero. We develop several approaches which allow us to extend well known boundedness results on the k th order rational difference equation to the setting of systems in certain cases.