Suucient conditions for controllability of semilinear integrodif-ferential systems in a Banach space are established. The results are obtained using the asymptotic xed-point theorem for k-set contractions .

The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...

We prove a generalization of Brouwer's famous xed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X one can always nd a point x 2 X such that kx ? f(x)k is less than a certain measure of discontinuity. Applications to artiicial neural nets, economic equilibria, and analysis are given.

In this paper we establish existence and regularity of positive solutions for a singular quasilinear elliptic system with competitive structure. The approach is based on comparison properties, a priori estimates and the Schauder’s …xed point theorem.

We establish a xed point theorem for a certain type of nonexpanding maps in Euclidean buildings, which is inspired by a theorem of La aille in p-adic Hodge theory [7, Theorem 3.2].

|Bifurcations of periodic orbits are studied for two-dimensional diieomorphisms close to a diieomorphism with the quadratic homoclinic tangency to a saddle xed point whose Jacobian is equal to one. Problems of the coexistence of periodic orbits of various types of stability are considered. INTRODUCTION It is well known that homoclinic bifurcations of two-dimensional diieomorphisms generally giv...

G. Gaeta Department of Mathematics, Loughborough University, Loughborough LE11 3TU (G.B.) [email protected] G. Marmo Dipartimento di Scienze Fisiche, Universit a di Napoli, and INFN, Sezione di Napoli, 80123 Napoli (Italy) Summary. We consider the classical problem of linearizing a vector eld X around a xed point. We adopt a nonperturbative point of view, based on the symmetry properties of lin...

Fixed-order computation rules, used by Prolog and most deductive database systems, do not suuce to compute the well-founded semantics 29] because they cannot properly resolve loops through negation. This inadequacy is reeected both in formulations of SLS-resolution 17, 23] which is an ideal search strategy, and in more practical strategies like SLG 5], or Well-Founded Ordered Search 27]. Typica...

We develop a model-checking algorithm for a logic that permits propositions to be deened using greatest and least xed points of mutually recursive systems of equations. This logic is as expressive as the alternation-free fragment of the modal mu-calculus identiied by Emerson and Lei, and it may therefore be used to encode a number of temporal logics and behavioral preorders. Our algorithm deter...

Results are obtained concerning the distribution of ranked relative lengths of excursions of a recurrent Markov process from a point in its state space whose inverse local time process is a stable subordinator. It is shown that for a large class of random times T the distribution of relative excursion lengths prior to T is the same as if T were a xed time. It follows that the generalized arc-si...