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We obtain sufficient conditions for the existence of at least three positive solutions for the equation x (t) + q(t)f (t, x(t), x (t)) = 0 subject to some boundary conditions. This is an application of a new fixed-point theorem introduced by Avery and Peterson .
In this paper, we prove the existence of nontrivial nonnegative classical time periodic solutions to the viscous diffusion equation with strongly nonlinear periodic sources. Moreover, we also discuss the asymptotic behavior of solutions as the viscous coefficient k tends to zero.
In this paper, we study a class of reaction-diffusion systems with time delays, which models the dynamics of predator-prey species. The global asymptotic convergence is established by the upper-lower solutions and iteration method in terms of the rate constants of the reaction function, independent of the time delays and the effect of diffusion
Taking the spatial diffusion into account, we consider a reaction-diffusion system that models three species on a growth-limiting, nonrepro-ducing resources in an unstirred chemostat. Sufficient conditions for the existence of a positive solution are determined. The main techniques is the Leray-Schauder degree theory.