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In this paper we applied the Squared Remainder Minimization Method (SRMM) to find analytic approximate polynomial solutions for Riccati differential equations. Two examples are included to demonstrated the validity and applicability of the method. The results are compared to those obtained by other methods. [ABSTRACT FROM AUTHOR]

In the present paper we extend the Homotopy Perturbation Method to find an approximate analytic solution for a nonlinear functional equation in a Banach space. While previously necessary and sufficient conditions were given for the existence of the solution only for the case of a non expansive operator, HPM allowed us to find solutions also for the case of an expansive operator T, as shown in the given example. [ABSTRACT FROM AUTHOR]

We define the notion of fibre stability of a closed set in a monotone global dynamical system and we give a characterization theorem by means of Lyapunov functions. [ABSTRACT FROM AUTHOR]

This paper considers a mathematical model of infectious disease of SIS type. We will analyze the problem of minimizing the cost of diseases trough medical treatment. Mathematical modeling of this process leads to an optimal control problem with a finite horizon. The necessary conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the steady state for a differential equations system. [ABSTRACT FROM AUTHOR]