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Communicated by J. BanasiakWe consider three species system, namely prey (roach), predator (pike) and plankton. We derive persistence and extinction conditions of the populations. Using coincidence degree theory, we determine conditions for which the system has a periodic solution.

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We consider a juvenile adult model with spatial structure and selective harvesting e¤ort on adult population .The dynamic behavior of the model system is investigated.The results indicate that competition between adults and cannibalism on juveniles do not a¤ect the population survival.Bioeconomic equilibrium and optimal harvesting are discussed.Finally some numerical simulations are given to illustrate theoretical results.

We discuss the existence of solutions of nonlinear third order ordinary differential equations with integral boundary conditions. We provide sufficient conditions on the nonlinearity and the functions appearing in the boundary conditions that guarantee the existence of at least one solution to our problem. We rely on the method of lower and upper solutions to generate an iterative technique, which is not necessarily monotone.