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Existence and uniqueness of positive periodic solutions of delayed Nicholson's blowflies models

Fei Long, Bingwen Liu (2012)

Annales Polonici Mathematici

This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays. By applying the coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, a totally new approach to proving the uniqueness of positive periodic solutions is proposed. In particular, an example is employed to illustrate the main results.

Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

Małgorzata Klimek, Marek Błasik (2012)

Open Mathematics

Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary...

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