### Existence and uniqueness of periodic solutions for a second-order nonlinear differential equation with piecewise constant argument.

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A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

By using Mawhin’s continuation theorem, the existence of even solutions with minimum positive period for a class of higher order nonlinear Duffing differential equations is studied.

Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form $${x}^{\text{'}}\left(t\right)+c{x}^{\text{'}}\left(t-\tau \right)=A\left(t,x\left(t\right)\right)x\left(t\right)+f\left(t,x\left(t-{r}_{1}\left(t\right)\right),\cdots ,x\left(t-{r}_{k}\left(t\right)\right)\right).$$

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