The paper examines a particular class of nonlinear integro-differential equations consisting of a Sturm-Liouville boundary value problem on the half-line, where the coefficient of the differential term depends on the unknown function by means of a scalar integral operator. In order to handle the nonlinearity of the problem, we consider a fixed point iteration procedure, which is based on considering a sequence of classical Sturm-Liouville boundary value problems in the weak solution sense. The existence of a solution and the global convergence of the fixed-point iterations are stated without resorting to the Banach fixed point theorem. Moreover, the unique solvability of the problem is discussed and several examples with unique and non-unique solutions are given.

We consider a particular second-order integrodifferential boundary value problem arising from the kinetic theory of dusty plasmas, and we provide information on the existence and other qualitative properties of the solution that have been essential in the numerical investigation.

The modeling of various physical questions in plasma kinetics and heat conduction lead to nonlinear boundary value problems involving a nonlocal operator, such as the integral of the unknown solution, which depends on the entire function in the domain rather than at a single point. This talk concerns a particular nonlocal boundary value problem recently studied in [1] by J.R.Cannon and D.J.Galiffa, who proposed a numerical method based on an interval-halving scheme. Starting from their results, we provide a more general convergence theorem and suggest a different iterative procedure to handle the nonlinearity of the discretized problem. References: [1] J.R.Cannon, D.J.Galiffa (2011) On a numerical method for a homogeneous, nonlinear, nonlocal, elliptic boundary problem, Nonlinear Analysis, Vol. 74, pp. 1702-1713.

In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number, when the infection incidence rate has a suitable monotone property.

In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays h 0 p(? )f (S(t), I (t - ?))d? under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f (S,I) and f (S,I)/I with respect to S >= 0 and I > 0, we extend the global stability result for an SIR epidemic model

We consider a weakly nonlinear system of the form (I + phi(x)A)x = p, where phi(x) is a real function of the unknown vector x, and (I + phi(x)A) is an M-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (I + phi(x(r))A)x(r + 1) = p, r = 0, 1, ... . The global convergence is proved by considering a related fixed-point problem.

We design and analyse a numerical method for the solution of a particular second order integro-differential boundary value problem on the semiaxis, which arises in the study of the kinetic theory of dusty plasmas. The method we propose represents a first insight into the numerical solution of more complicated problems and consists of a discretization of the differential and integral terms and of an iteration process to solve the resulting non-linear system. Under suitable hypotheses we prove the convergence. We will show the characteristics of the method by means of some numerical simulations.

In this paper we investigate the permanence of a system and give a sufficient condition for the endemic equilibrium to be globally asymptotically stable, which are the remaining problems in our previous paper (G. Izzo, Y. Muroya, A. Vecchio, A general discrete time model of population dynamics in the presence of an infection, Discrete Dyn. Nat. Soc. (2009), Article ID 143019, 15 pages. doi:10.1155/2009/143019.) (C) 2011 Elsevier Ltd. All rights reserved.

Numerical solution of two delays Volterra Integral Equations is considered and the stability is studied on a nonlinear test equation by carrying out a parallel investigation both on the continuous and the discrete problem.