Global behavior for a diffusive predator-prey model with stage structure and nonlinear density restriction. I: The case in .
Global bifurcation for second-order Neumann problem with a set-valued term.
Global canonical forms of linear differential equations
Global error control for the continuous Galerkin finite element method for ordinary differential equations
Global existence and asymptotic behavior of solution of second-order nonlinear impulsive differential equations.
Global existence and boundedness for quasi-variational systems.
Global Gronwall estimates for integral curves on Riemannian manifolds.
We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.
Global optimality conditions for a dynamic blocking problem
The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set R(t) ⊂ ℝ2, described as the reachable set for a differential inclusion. To restrict its growth, a barrier Γ can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification of blocking arcs. Moreover, we derive local and...
Global optimality conditions for a dynamic blocking problem
The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set R(t) ⊂ ℝ2, described as the reachable set for a differential inclusion. To restrict its growth, a barrier Γ can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification...
Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method
Global stability of steady solutions for a model in virus dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Global Stability of Steady Solutions for a Model in Virus Dynamics
We consider a simple model for the immune system in which virus are able to undergo mutations and are in competition with leukocytes. These mutations are related to several other concepts which have been proposed in the literature like those of shape or of virulence – a continuous notion. For a given species, the system admits a globally attractive critical point. We prove that mutations do not affect this picture for small perturbations and under strong structural assumptions. Based on numerical...
Global theory of ordinary linear homogeneous differential equations in the real domain - II.
Global theory of ordinary linear homogeneous differential equations in the real domain -I.
Global transformations of linear differential equations.
Globally convergent differential procedures for solving nonlinear systems of equations
Groupes algébriques et équations différentielles linéaires
Growth estimates for non-oscillatory solutions of a non-linear differential equation
Growth model with migration: structure of optimal saving rates