A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.
Étant donné un système d’équations différence-différentielles à coefficients constants en deux variables, où les retards sont commensurables, de la forme : , , si le système n’est pas redondant (i.e. est discrète dans ), toute solution du système admet une représentation , où , et est une solution du système . La série est de plus convergente dans après un groupement de termes indépendant de la solution .
Continuing the idea of Part I, we deal with more involved pseudogroup of transformations , , applied to the first order differential equations including the underdetermined case (i.e. the Monge equation ) and certain differential equations with deviation (if is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the...