Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Perturbed nonlinear elliptic Neumann problem involving anisotropic Sobolev spaces with variable exponents
Full text linkIn this paper we study the existence of infinitely many weak solutions of the following perturbed Kirchhoff-type non-homogeneous Neumann problem
by applying technical approach based on critical points theorem due to B. Ricceri in a reflexive anisotropic Sobolev spaces. We use some suitable assumptions on the right had side but without using log-Ho ̈lder continu- ous condition
On a question about non-uniqueness of global minima
Full text linkLet X be a topological space, I and J be sequentially l.s.c. real functions on X such that J is non-negative with sequentially compact sub-levels, and I/J is not bounded from below outside the sublevel J−1([0,c[) of J for some c>0. Is it true that for any large enough λ and any increasing l.s.c. real function φ the function x → I(x)+λJ(x)+μφ◦J(x) has at least two global minima for some positive μ? We give a positive answer to this question assuming that I + λ J + μ ◦φ has sequentially compact sublevels for some λ and all μ > 0
Estimates on counting functions associated to some hyperbolic operators and spectral properties
Full text linkWe study the distribution of the eigenvalues of a linear operator associated to a hyperbolic partial differential equation with periodic boundary conditions. Using some recent results concerning the distributions of the values of indefinite quadratic forms at integers, we are able to derive the equidistribution of the eigenvalues relatively to the Lebesgue measure with exact asymptotics. Also we provide an asymptotic lower bound in the rational case
A Liapunov function for the initial-boundary value problem modeling the microwave heating and its consequences on the formation of hot-spots
Full text linkWe prove that if the electricconductivity σ is grater than the adsorpbidity q and the condition of perfect insulation holds on the boundary of the specimen heated, the functional
is a Liapunov function for the initial boundary value problem modelling the microwave heating. If σ and q are constants the formation of hotspots is impossible
A Transcendence of some infinite series
No full textIn the present paper and as an application of J. Hancl criterion for transcendental sequences which gave a sufficient conditions that will assure us that a series of positive rational terms is a transcendental number. With the same conditions, we establish a transcendental measure of ∑∞n=1 1/a
Tensor join of hypergraphs and its spectra
Full text linkIn this paper, we introduce three operations on hypergraphs by using tensors. We show that these three formulations are equivalent and we commonly call them as the tensor join. We show that any hypergraph can be viewed as a tensor join of hypergraphs. Tensor join enable us to obtain several existing and new classes of operations on hypergraphs. We compute the adjacency, the Laplacian, the normalized Laplacian spectrum of weighted hypergraphs constructed by this tensor join. Also we deduce some results on the spectra of hypergraphs in the literature. As an application, we construct several pairs of the adjacency, the Laplacian, the normalized Laplacian cospectral hypergraphs by using the tensor join
The distributional divergence of horizontal vector fields vanishing at infinity on Carnot groups
Full text linkWe define a BV-type space in the setting of Carnot groups (i.e., simply connected Lie groups with stratified nilpotent Lie algebra) that allows one to characterize all distributions F for which there exists a continuous horizontal vector field Φ, vanishing at infinity, that solves the equation divHΦ = F . This generalizes to the setting of Carnot groups some results by De Pauw and Pfeffer, [13], and by De Pauw and Torres, [14], for the Euclidean setting
Real circles tangent to 3 conics
Full text linkIn this paper we study circles tangent to conics. We show there are generically 184 complex circles tangent to three conics in the plane and we characterize the real discriminant of the corresponding polynomial system. We give an explicit example of 3 conics with 136 real circles tangent to them. We conjecture that 136 is the maximal number of real circles. Furthermore, we implement a hill-climbing algorithm to find instances of conics with many real circles, and we introduce a machine learning model that, given three real conics, predicts the number of circles tangent to these three conics
Hahn multiplicative calculus
Full text linkIn this study, Hahn multiplicative calculus was introduced and as an application of this subject, the classical Sturm--Liouville problem was examined under this structure
On a second order discrete problem
Full text linkBy using variontional methods, we establish criteria for the existence of at least three solutions to a second order discrete problem with two parameters. Applications of the maintheorem to several special cases of the problem are discussed and two examples are included to illustrate the results. This paper extends and complements some of our early work on related problems