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This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. Copyright © 2014 John Wiley & Sons, Ltd.

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In this paper we study the Lotka-Volterra models with fractional Laplacian. For that, we study in detail the logistic problem and show that the sub-supersolution method works for the scalar problem and in case of systems as well. We apply this method to show existence and non-existence of positive solutions in terms of the system parameters.