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Showing papers in "Ricerche Di Matematica in 2011"


Journal ArticleDOI
TL;DR: In this paper, the existence of positive ground states with minimal energy was shown in the case of an elliptic system and satisfying suitable assumptions, but not requiring any symmetry property on them.
Abstract: In this paper we consider the following elliptic system in $${\mathbb{R}^3}$$ $$\qquad\left\{\begin{array}{ll}-\Delta u+u+\lambda K(x)\phi u=a(x)|u|^{p-1}u \quad &x \in {\mathbb{R}}^{3}\\ -\Delta \phi=K(x)u^{2} \quad &x \in {\mathbb{R}}^{3}\end{array}\right.$$ where λ is a real parameter, $${p\in (1, 5)}$$ if λ < 0 while $${p\in (3, 5)}$$ if λ > 0 and K(x), a(x) are non-negative real functions defined on $${\mathbb{R}^3}$$ . Assuming that $${\lim_{|x|\rightarrow+\infty}K(x)=K_{\infty} >0 }$$ and $${\lim_{|x|\rightarrow+\infty}a(x)=a_{\infty} >0 }$$ and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive ground states, namely the existence of positive solutions with minimal energy.

72 citations


Journal ArticleDOI
TL;DR: In this paper, the existence of minimizers of the functional Φ in each 3-homotopy class of smooth maps was proved for a triangulation of a Riemannian manifold.
Abstract: Let (M, g) and (N, h) be Riemannian manifolds without boundary and let f : M → N be a smooth map. Let $${\|f^*h\|}$$ denote the norm of the pullback metric of h by f. In this paper, we consider the functional $${{\Phi (f) = \int_M \|f^*h\|^2 dv_g}}$$ . We prove the existence of minimizers of the functional Φ in each 3-homotopy class of maps, where maps f 1 and f 2 are 3-homotopic if they are homotopic on the three dimensional skeltons of a triangulation of M. Furthermore, we give a monotonicity formula and a Bochner type formula.

31 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the symplectic dual of a Desarguesian spread of PG(5, q), q odd is a generalized twisted field arising from generalized twisted fields.
Abstract: In this paper we show that starting from a symplectic semifield spread $${\mathcal{S}}$$ of PG(5, q), q odd, another symplectic semifield spread of PG(5, q) can be obtained, called the symplectic dual of $${\mathcal{S}}$$ , and we prove that the symplectic dual of a Desarguesian spread of PG(5, q) is the symplectic semifield spread arising from a generalized twisted field. Also, we construct a new symplectic semifield spread of PG(5, q) (q = s 2, s odd), we describe the associated commutative semifield and deal with the isotopy issue for this example. Finally, we determine the nuclei of the commutative pre-semifields constructed by Zha et al. (Finite Fields Appl 15(2):125–133, 2009).

29 citations


Journal ArticleDOI
TL;DR: In this article, the Laplace transform of the transition probability density function in the presence of pairs of reflecting boundaries is obtained for one-dimensional time-homogeneous diffusion processes with absorbing and/or reflecting boundaries.
Abstract: A comprehensive outline is presented for obtaining the Laplace transforms of the transition probability density functions and of the first-passage-time densities for one-dimensional time-homogeneous diffusion processes in the presence of absorbing and/or reflecting boundaries. In particular, the Laplace transform of the transition probability density function in the presence of pairs of reflecting boundaries are explicitly obtained. Symmetric diffusion processes are then specifically considered and explicit closed-form relations are then obtained for the hyperbolic diffusion process in the presence of absorbing and/or reflecting boundaries. The special cases of the Brownian motion and of the Hongler process are finally analyzed.

18 citations


Journal ArticleDOI
TL;DR: In this article, the exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail.
Abstract: Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space–time model are examined in detail. Firstly, for scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient $${R_{\epsilon j}}$$ on the background of the de Sitter space–time model is analyzed. It is shown that the determination of $${R_{\epsilon j}}$$ requires an additional constrain on quantum numbers $${\epsilon \rho / \hbar c \gg j}$$ , where ρ is a curvature radius. When taken into account of this condition, the $${R_{\epsilon j}}$$ vanishes identically. It is claimed that the calculation of the reflection coefficient $${R_{\epsilon j}}$$ is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space–time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.

15 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied warped product submanifolds of cosymplectic manifolds and obtained a characterization result for the warped product of the type n = 2.
Abstract: In the present paper, we study warped product CR-submanifolds of cosymplectic manifolds. It is shown that the warped product of the type \({N_\perp\times{_f}N_T}\) is trivial and obtain a characterization result for the warped product of the type \({N_T\times{_f}N_\perp}\) , where NT and \({N_\perp}\) are invariant and anti-invariant submanifolds of a cosymplectic manifold \({\bar M}\) , respectively.

13 citations


Journal ArticleDOI
TL;DR: In this paper, the Taylor's expansions around equilibrium or the transition to subsystems were used to obtain the exact closure to the conditions arising from the entropy principle and the material objectivity principle.
Abstract: In this article we aim to furnish arguments for further considerations on some procedures commonly used in Extended Thermodynamics, such as the Taylor’s expansions around equilibrium or the transition to subsystems. The initial impulse for these considerations lies in the fact that we have found, for a 14 moments model, the exact closure to the conditions arising from the entropy principle and the material objectivity principle, without using Taylor’s expansions. These generated some problems; one of these concerns the relationship between system and subsystems, another one concerns the convexity of entropy and hyperbolicity; a third problem deals with the correct moments to be used as independent variables, those suggested by the classical limit of the relativistic moment theory. We will give suggestions for the solution of these problems.

9 citations


Journal ArticleDOI
TL;DR: In this paper, the generalized (G′/G)-expansion method was modified to obtain new traveling wave solutions for nonlinear differential equations, and the generalized Zakharov equations were chosen to illustrate the method in detail.
Abstract: In this paper, we modified the so-called generalized (G′/G)-expansion method to obtain new traveling wave solutions for nonlinear differential equations. The generalized Zakharov equations are chosen to illustrate the method in detail.

6 citations


Journal ArticleDOI
TL;DR: In this paper, a classical result of Amick (Acta Math 161:71−130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier-Stokes equations in the plane is extended to Lipschitz domains.
Abstract: A classical result of Amick (Acta Math 161:71–130, 1988) on the nontriviality of the symmetric Leray solutions of the steady-state Navier–Stokes equations in the plane is extended to Lipschitz domains. This results is compared with the famous Stokes paradox of linearized hydrodynamics and applied to a mixed problem of some interest in the applications.

6 citations


Journal ArticleDOI
TL;DR: The dynamics of some algal allelopathic competitions taking place in a laboratory chemostat-like environment are analyzed in this article, where the main results concern the global asymptotic stability of some biologically meaningful steady-state solutions and have been obtained by means of limiting systems theory and construction of suitable Liapunov functions.
Abstract: The dynamics of some algal allelopathic competitions taking place in a laboratory chemostat-like environment are analyzed. Our main results concern the global asymptotic stability of some biologically meaningful steady-state solutions and have been obtained by means of limiting systems theory and construction of suitable Liapunov functions. In particular one of these results completely explains the outcome of several experiments recently performed and illustrated in Fergola et al. (Ecol Model 208:205–214, 2007) on the competition between C. vulgaris and P. subcapitata. Numerical simulations confirm the analytical results and show that saddle-node bifurcation phenomena can appear.

4 citations


Journal ArticleDOI
TL;DR: In this article, the existence and physical uniqueness of the restricted evolution problem in general relativity was proved for both harmonic and generic adapted coordinates in order to prove the existence of solution in both systems of coordinates.
Abstract: The existence and physical uniqueness is proved for the restricted evolution problem in general relativity. Precisely, the Einstein equations for the gravitational field are analyzed in harmonic and generic adapted coordinates in order to prove the existence and uniqueness of solution in both systems of coordinates.

Journal ArticleDOI
TL;DR: In this article, the authors presented new definitions which are a natural combination of the definition for asymptotically equivalence and Δ m istg -lacunary strongly summable with respect to a modulus f.
Abstract: This paper presents new definitions which are a natural combination of the definition for asymptotically equivalence and Δ m -lacunary strongly summable with respect to a modulus f. Using this definitions we have proved the (f, Δ m )-asymptotically equivalence and Δ m -lacunary statistical asymptotically equivalence analogues of theorems of Tripathy and Et (Stud Univ Babes-Bolyai Math (1):119–130, 2005) and Colak’s theorems (Filomat 17:9–14, 2003).

Journal ArticleDOI
TL;DR: In this article, it was shown that there exists a semi-local Prufer ring T with quotient field K such that [R, S] is a partially ordered set.
Abstract: Let \({R\subset S}\) be an extension of integral domains and let [R, S] be the set of intermediate rings between R and S ordered by inclusion. If (R, S) is normal pair and [R, S] is finite, we do prove that there exists a semi-local Prufer ring T with quotient field K such that \({[R,S]\cong \lbrack T,K]}\) (as a partially ordered set). Consequently, any problem relative to the finiteness conditions in [R, S] can be investigated in the particular case where R is a semi-local Prufer ring with quotient field S.

Journal ArticleDOI
TL;DR: In this article, a class of semilinear elliptic variational inequalities on H1(Ω) space is considered and the existence of solutions is proved with the aid of the mountain pass principle and the Ekeland variational principle.
Abstract: In this note we consider a class of semilinear elliptic variational inequalities on H1(Ω) space. With the aid of the mountain-pass principle and the Ekeland variational principle we prove the existence of solutions.

Journal ArticleDOI
TL;DR: In this article, the Riemann-Silberstein-Majorana-Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix formalism, and four types of formal solutions of the Maxwell equations on the base of scalar D'Alembert solutions are constructed.
Abstract: The Riemann–Silberstein–Majorana–Oppenheimer complex approach to the Maxwell electrodynamics is investigated within the matrix formalism. Within the squaring procedure we construct four types of formal solutions of the Maxwell equations on the base of scalar D’Alembert solutions. General problem of separating physical electromagnetic solutions in the linear space λ0Ψ0 + λ1Ψ1 + λ2Ψ2 + λ3Ψ3 is investigated, the Maxwell equations reduce to a new form including parameters λ a . Several particular cases, plane waves and cylindrical waves, are considered in detail. Possible extension of the technique to a curved space–time models is discussed.

Journal ArticleDOI
TL;DR: In this article, a simple way to determine purity for a B(n)-group contained in a completely decomposable group was proposed, based on the concept of decomposition.
Abstract: We show a simple way to determine purity for a B(n)-group contained in a completely decomposable group.

Journal ArticleDOI
TL;DR: In this paper, it was shown that if q = ph, p a prime, do not exist sets with |U| = qk and 1 < k < n, determining N directions where q > 2 is even.
Abstract: We prove that if q = ph, p a prime, do not exist sets \({U {\subseteq} AG(n,q)}\), with |U| = qk and 1 < k < n, determining N directions where $$ \frac{{q^k} - 1}{p - 1} < N \le \frac{q+3}{2} q ^{k-1}+ q^{k-2} +\dots+q{^2} + q $$ when q is odd and $$ \frac{{q^k} - 1}{3} < N \le \frac{q+3}{2} q ^{k-1}+ q^{k-2} +\dots+q{^2} + q $$ when q > 2 is even.


Journal ArticleDOI
TL;DR: In this paper, the Ricceri problem for elliptic systems with variable exponents was studied and the existence of at least three nontrivial solutions was obtained by using an equivalent variational approach to a recent RICceri's three critical points theorem.
Abstract: In this paper, we study a Neumann problem for elliptic systems with variable exponents. We obtain the existence of at least three nontrivial solutions by using an equivalent variational approach to a recent Ricceri’s three critical points theorem (Ricceri in Nonlinear Anal TMA 70:3084–3089, 2009).