Ricerche di Matematica

In this paper, we establish the existence of multiple solutions for nonhogeneous singular elliptic equations involving critical Caffarelli–Kohn–Nirenberg exponent, by using Ekeland’s Variational Principle and Mountain Pass Theorem without Palais Smale conditions.

We consider the following anisotropic problem, with singular nonlinearity having a variable exponent $$\begin{aligned} \left\{ \begin{array}{ll} -\sum \limits _{i=1}^{N}\partial _{i}\left[ \left| \partial _{i}u\right| ^{p_{i}-2}\partial _{i}u\right] =\frac{f}{u^{\gamma (x) }} &{} \quad in~\Omega , \\ u=0 &{} \quad on~\Omega , \\ u\ge 0 &{} \quad in~\Omega ; \end{array} \right. \end{aligned}$$ where $$\Omega $$ is a bounded regular domain in $${\mathbb {R}}^{N}$$ and $$\gamma (x)>0$$ is a smooth function, having a convenient behavior near $$\partial \Omega .$$ f is assumed to be a non negative function belonging to a suitable Lebesgue space $$L^{m}\left( \Omega \right) .$$ We will also assume without loss of generality that $$2\le p_{1}\le p_{2}\le \cdots \le p_{N}.$$ Using approximation techniques, we obtain existence and regularity of positive solutions to the considered problem.

We study the complete Steenrod algebra $${{\hat{{\fancyscript A}}}}$$ for an odd prime p and its relations with the generalized Dickson algebra on infinitely many generators, as a $${\mathbb{Z} [\frac{1}{p}]}$$ -graded algebra.

Let $$f : A \rightarrow B$$ be a ring homomorphism and J be an ideal of B. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani’s and Yassemi’s work (see Maimani and Yassemi in J Pure Appl Algebra 212(1):168–174, 2008). Furthermore, we investigate the transfer of Prüfer domain concept to commutative rings with zero divisors in the amalgamation of A with B along J with respect to f (denoted by $$A\bowtie ^fJ),$$ introduced and studied by D’Anna et al. (Commutative algebra and its applications, Walter de Gruyter, Berlin, 2009, J Pure Appl Algebra 214:1633–1641, 2010). Our results recover well known results on duplications. The main applications constist in the construction of new original classes of Prüfer rings that are not Gaussian and Prüfer rings with weak global dimension strictly greater than 1.

The transfer of heat and mass by convection in fluid layers is a challenging task as it can be driven by different factors. In the present paper the coupled action of viscosity and thermal diffusivity, both stratified, is investigated. The thermal conduction steady state is found and it is shown that: (1) steady convection occurs; (2) linear stability guarantees nonlinear asymptotic exponential energy stability and global attractivity.

This paper investigates an SIR model with the following properties: (i) demographics are present. (ii) The fraction vaccinating at any time is dependent on past levels of disease prevalence with distributed delay. (iii) The maximum fraction vaccinating is bounded below one by medical contraindications or unshakeable beliefs among a sub-set of the population that the vaccination is not beneficial. (iv) Disease transmissibility is higher when school is in session than when it is not. Our main findings are that the time series of prevalence can exhibit irregular inter-epidemic intervals, and the profile of outbreaks can be highly variable over time—sometimes exhibiting single large peaks and sometimes clusters of closely-spaced lesser peaks.

We review the recently developed theory of extended thermodynamics (ET) of real gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting near-equilibrium approximation. We discuss the polytropic and non-polytropic cases of rarefied polyatomic gases in detail, including the closure via nonlinear molecular ET.