Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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On some semilinear equations
Get PDFThe results presented here are obtained with Lucio Boccardo and regards some nonlinear elliptic problems.[omissis
Flocks, ovoids and generalized quadrangles
Get PDFIn this paper we will discuss some of the connections between flocks of quadratic cones, ovoids of PG(3, q) and generalized quadrangles
Families of curves and variation in moduli
Get PDFIn this paper we study the class of smooth complex projective varieties B such that any modular morphism B → M_g is constant for any g ≥ 2, giving structural properties and examples. Then we investigate the concept of the moduli dimension of a variety B; we bound it by the dimension of the maximal rationally connected quotient of B. In the end we consider also (generically smooth) families of curves of compact type over rational and elliptic curves
Three solutions for a Neumann boundary value problem involving the p-Laplacian
Get PDFIn this note we prove the existence of an open interval ]λ\u27, λ"[ for each λ of which a Neumann boundary value problem involving the p-Laplacian and depending on λ admits at least three solutions. The result is based on a recent three critical points theorem
Searching and sweeping graphs: a brief survey
Get PDFThis papers surveys some of the work done on trying to capture an intruder in a graph. If the intruder may be located only at vertices, the term searching is employed. If the intruder may be located at vertices or along edges, the term sweeping is employed. There are a wide variety of applications for searching and sweeping. Old results, new results and active research directions are discussed
How to use Rédei polynomials in higher dimensional spaces
Get PDFThe problem for which Rédei introduced the polynomial R(T , S) was that of determining those functions over a finite field that determine few directions
Multipartite graph decomposition: cycles and closed trails
Get PDFThis paper surveys results on cycle decompositions of complete multipartite graphs (where the parts are not all of size 1, so the graph is not K_n ), in the case that the cycle lengths are “small”. Cycles up to length n are considered, when the complete multipartite graph has n parts, but not hamilton cycles. Properties which the decompositions may have, such as being gregarious, are also mentioned
An identification problem for some degenerate differential equation
Get PDF We are concerned with a degenerate first order identification problem in a Banach space. Suitable hypotheses on the involved operators are made in order to reduce the given problem to a non-degenerate case. Some applications to partial differential equations are indicated extending well known results in the regular case
Perron conditions for exponential expansiveness of one-parameter semigroup
Get PDFWe present a new approach for the theorems of Perron type for exponential expansiveness of one-parameter semigroups in terms of l^p(N, X) spaces. We prove that an exponentially bounded semigroup is exponentially expansive if and only if the pair (l^p (N, X), l^q(N, X)) is completely admissible relative to a discrete equation associated to the semigroup, where p, q ∈ [1, ∞), p ≥ q. We apply our results in order to obtain very general characterizations for exponential expansiveness of C_0-semigroups in terms of the complete admissibility of the pair (L^ p (R_+ , X), L^ q (R_+ , X)) and for exponential dichotomy, respectively, in terms of the admissibility of the pair (L^p(R_+,X), L^q(R_+,X))