Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay.
In this paper, there are derived sufficient conditions for exponential and asymptotic stability of differential and difference systems.
We study the asymptotic behavior of the solutions of a scalar convolution sum-difference equation. The rate of convergence of the solution is found by determining the asymptotic behavior of the solution of the transient renewal equation.
Let X be an arbitrary Abelian group and E a Banach space. We consider the difference-operators ∆n defined by induction:(∆f)(x;y) = f(x+y) - f(x), (∆nf)(x;y1,...,yn) = (∆n-1(∆f)(.;y1)) (x;y2,...,yn)(n = 2,3,4,..., ∆1=∆, x,yi belonging to X, i = 1,2,...,n; f: X --> E).Considering the difference equation (∆nf)(x;y1,y2,...,yn) = d(x;y1,y2,...,yn) with independent variable increments, the most general solution is given explicitly if d: X x Xn --> E is a given bounded function. Also the...
We consider the summation equation, for , in the case where the map may change sign; here is a parameter, which may be understood as the order of an associated discrete fractional boundary value problem. In spite of the fact that is allowed to change sign, by introducing a new cone we are able to establish the existence of at least one positive solution to this problem by imposing some growth conditions on the functions and . Finally, as an application of the abstract existence result,...
We consider the functional equation f(z+σ) - f(z) = g(z) where σ is a complex number, f and g are entire functions of a complex variable z, with growth conditions. We prove the existence of certain types of solutions of this equation by an a priori estimate method in certain weighted L2-spaces.
On étudie les phénomènes de retard à la bifurcation et de butée pour des systèmes discrets lents-rapides du plan. On donne une explication géométrique de ces phénomènes basée sur l’examen de fonctions reliefs. On démontre ensuite l’existence et la vie brève des longs canards, qui sont des trajectoires ne présentant pas de butée. Trois exemples illustrent ces phénomènes. Le premier expose la problématique, le second permet une expérimentation de l’étude théorique sur les longs canards, le troisième...
Le sujet de cet article est l’étude des solutions continues sur ou holomorphes sur à valeurs complexes de systèmes de deux équations aux différences à coefficients polynomiauxAvec des hypothèses convenables sur les pas des équations (de nature algébrique et géométrique dans le cas complexe), on montre que ces solutions sont des polynômes exponentiels ou des quotients de polynômes exponentiels par des polynômes. Ces résultats prolongent ceux de J.-P. Bézivin et F. Gramain d’une part et de N. Brisebarre...