Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Periodic solutions for second order Hamiltonian systems
Get PDFIn this paper we present some recent multiplicity results for a class of second order Hamiltonian systems. Exploiting the variational structure of the problem, it will be shown how the existence of multiple, even infinitely many, periodic solutions can be assured
Resonance and Landesman-Lazer conditions for first order systems in R^2
Get PDFThe first part of the paper surveys the concept of resonance for T-periodic nonlinear problems. In the second part, some new results about existence conditions for nonlinear planar systems are presented. In particular, the Landesman-Lazer conditions are generalized to systems in R^2 where the nonlinearity interacts with two resonant Hamiltonians. Such results apply to second order equations, generalizing previous theorems by Fabry [4] (for the undamped case), and Frederickson-Lazer [9] (forthe case with friction). The results have been obtained with A. Fonda, and have been published in [8]
Remark on the number of solutions in the thermistor problem
Get PDFIn this paper we study the nonlocal thermistor problem which models two simple electrical circuits. We prove that under certain assumptions on the electrical conductivity multiple states of thermal and electrical equilibria (typically three) are possible. All mathematical methods used are elementary
Some results associated with a generalized basic hypergeometric function
Get PDFIn this paper, we define a q-extension of the new generalized hypergeometric function given by Saxena et al. in [13], and have investigated the properties of the above new function such as q-differentiation and q-integral representation. The results presented are of general character and the results given earlier by Saxena and Kalla in [14], Virchenko, Kalla and Al-Zamel in [15], Al-Musallam and Kalla in [2, 3], Kobayashi in [7, 8], Saxena et al. in [13], Kumbhat et al. in [11] follow as special cases
Essentially hyponormal operators with essential spectrum contained in a circle
Get PDFIn this paper two results are given . It is proved that if the essential spectrum σ(π(T)) of the bounded hyponormal operator T is contained in a circle, then T is essentially normal operator. Based on this result it is proved that if T∈ L(H) with ind T = 0 then T = λU + K (where λ ∈ R^+, U is a unitary operator and K is a compact operator) if and only if TT^∗ is quasi-diagonal with respect to any sequence {P_n } in PF(H) such that Pn → I, strongly
A path crossing lemma and applications to nonlinear second order equations under slowly varyng perturbations
Get PDFWe present some recent results on the existence of periodic solutions and chaotic like dynamics for second order scalar nonlinear ODEs. The equations under consideration belong to a simple class of perturbed planar Hamiltonian systems with slowly varying periodic coefficients, a typical example being given by the pendulum equation with moving support. Although there is already a broad literature on this subject, our approach, based on the concept of stretching along the paths, appears new in this context. In particular, our method is global in nature and stable with respect to small perturbations of the coefficients. Thus it applies even when some small friction terms are inserted into the equations. The main tool on which all our results are based is a topological lemma (that we call path crossing lemma) which was already implicitly used by Poincaré (1883-1884) [51], as well as by Butler (1976) [8] and Conley (1975) [12] and subsequently “rediscovered” and applied in many different contexts. For this reason, the first part of this paper is devoted to a detailed exposition of the Crossing Lemma and its connections with other topological results
Summation formulae for basic hypergeometric functions via fractional q-calculus
Get PDFThe object of this paper is to illustrate how the q-fractional calculus approach can be employed to derive a number of summation formulae for the generalized basic hypergeometric functions of one and more variables in terms of the q-gamma functions
On sequences of integers for Hankel planes Σ of P^m
No full textFor a vector space R ⊆ k^{m+1} of dimension r + 1 on the algebraically closed field k we determine, for any i ≤ r, the possible numbers of Hankel i−planes contained in the r−plane P(R), linear space in P^m
On the symmetric block design with parameters (153, 57, 21)
Get PDFIn this paper it is proved that:A) Up to isomorphism and duality there are exactly two possible orbital structures for a putative symmetric block design with parameters (153, 57, 21) constructed using the Frobenius group F_{17·16}B) Up to isomorphism and duality there are exactly 16 possible orbital structures for a putative symmetric block design with parameters (153, 57, 21) constructed using the collineation group G
Structure d\u27algèbre de Banach sur l\u27espace à poids L_ω^p(G)
Get PDFLet G be a locally compact group and ω be a weight on G. For p ∈ ]1, +∞ [, we give a necessary and sufficient condition, on ω, for L_ω^p (G) to be a Banach algebra. The case where ω is biinvariant under a subgroup K of G is also considered