Multiplicity of standing wave solutions of nonlinear Schrödinger equations with electromagnetic fields

In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schr?dinger equations with electromagnetic fields

On Separation of Points from Additive Subgroups of Banach Spaces by Continuous Characters and Positive Definite Functions

Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions: (ws) if , then x is weakly separated from G; (ps) if , then x is -separated from G; (wp) if Tx is -separated from T(G), then x is weakly separated from G. By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .      

Periodic parabolic problems with concave and convex nonlinearities

Let be a smooth bounded domain, let a, b be two functions that are possibly discontinuous and unbounded with a ≥ 0 in and b > 0 in a set of positive measure and let 0 < p < 1 < q. We prove that there exists some 0 < Λ < ∞ such that the nonlinear Dirichlet periodic parabolic problem in has a positive solution for all 0 < λ < Λ and that there is no positive solution if λ > Λ. In some cases we also show the existence of a minimal solution for all 0 < λ < Λ and that the solution u _λ can be chosen such that λ → u _λ is differentiable and increasing. We also give some upper and lower estimates for such a Λ. All results remain true for the analogous elliptic problems. Partially supported by CONICET, Secyt-UNC, ANPCYT and Agencia Cordoba Ciencia     

Multivalued evolution equations with nonlocal initial conditions in Banach spaces

We prove the existence of integral solutions to the nonlocal Cauchy problem in a Banach space X, where is m-accretive and such that –A generates a compact semigroup, has nonempty, closed and convex values, and is strongly-weakly upper semicontinuous with respect to its second variable, and . The case when A depends on time is also considered.      

Cylinder Multipliers Associated with a Convex Polygon

In this paper we prove that sharp weak-type estimates for the maximal operators associated with a cylindric distance function associated with a convex polygon on when 2/3 < p < 1 and , or when p = 2/3 and . This work was supported (in part) by research funds from Chosun University, 2007.     

A characterization of free generating sets in MV-algebras

MV-algebras are a generalization of Boolean algebras. As is well known, a free generating set for a Boolean algebra is characterized by the following simple algebraic condition: whenever A and B are finite disjoint subsets of X then . Our aim in this note is to give a similar characterization of free generating sets in MV-algebras. Received January 30, 2005; accepted in final form March 13, 2007.     

Group Algebras: Normal Subgroups and Ideals

The standard correspondence between the normal subgroups of the group G and some ideals of the group algebra FG is described. There is the problem of what we can say (or even prove) about a two-sided ideal of that does not contain any element of the form 1 − g ≠ 0, g ∈G of the standard basis of the augmentation ideal of . The main part of the argument of [2] yields the insight that, for such an ideal I there exists an expansion such that the ideal J of spanned by I contains an element 1 − h, h ∈ H \ G. Using the ideas of [2], we construct -thick groups H such that for every ideal J ≠ (0) of there are elements 1 − h ≠ 0 in J. This construction allows many variations. Examples of simple -thick groups were pointed out in [2]. A natural class of (in general non-simple) -full groups are the normal sections of the groups

On the stability of <Emphasis Type="Italic">t</Emphasis>-convex functions

Summary.  A real-valued function f defined on an open convex set is called (d, t)-convex if it satisfies

Selections of lattice-ordered Groups

It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail. Received March 7, 2006; accepted in final form August 29, 2006.     

Linear Independence of Values of a Certain Lambert Series

Let K be or an imaginary quadratic number field, and q K an integer with |q| > 1. We give a quantitative version of the linear independence over K of the three numbers 1, , and an equivalent power series version. We also mention several open problems. Received: February 5, 2007. Revised: April 18, 2007.     

Numerical bifurcation and stability analysis for steady-states of reaction diffusion equations

Solutions of a semilinear elliptic boundary value problem, (with bounded below) can be put into a one-to-one correspondence with zeros of a function . Often d is small. The function is called the bifurcation function. It can also be shown that the eigenvalues of the matrix characterize the stability properties of the solutions of the elliptic problem as rest points of . A finite element method that can be used for computing B and B _c has recently been proposed. An overview of these results and the finite element method is given. This revised version was published online in June 2006 with corrections to the Cover Date.     

Asymptotic behaviour for a nonlocal diffusion equation on a lattice

In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.      

Rigidity of hyperstable complexes

A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type. Received: 17 November 2006     

Closed polynomials and saturated subalgebras of polynomial algebras

The behavior of closed polynomials, i.e., polynomials such that the subalgebra is integrally closed in , is studied under extensions of the ground field. Using some properties of closed polynomials, we prove that, after shifting by constants, every polynomial can be factorized into a product of irreducible polynomials of the same degree. We consider some types of saturated subalgebras , i.e., subalgebras such that, for any , a generative polynomial of f is contained in A. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1587–1593, December, 2007.     

On meromorphic solutions of f 3 + g 3 = 1

We show that meromorphic solutions f, g of f ³ + g ³ = 1 in must be constant, if and have the same zeros (counting multiplicities). Received: 12 March 2007     

A singular Moser-Trudinger embedding and its applications

Let Ω be a bounded domain in , we prove the singular Moser-Trudinger embedding: if and only if where and . We will also study the corresponding critical exponent problem.     

Isometries and direct decompositions of pseudo MV-algebras

In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) there exists an internal direct decomposition of with commutative such that and for each x ∈ A. On the other hand, if is an internal direct decomposition of a pseudo MV-algebra = (A, ⊕, ⁻, ^∼, 0, 1) with commutative, then the mapping g: A → A defined by is an isometry in and .      

Structure on Powers of <Emphasis Type="Italic">p</Emphasis>-Hyponormal and log-Hyponormal Operators

Inspired by the problem of powers of hyponormal operators, this paper is to discuss the structure on powers of p-hyponormal and log-hyponormal operators. The structure on powers of operators consists of same-side structure and different-side structure. The same-side structure means relations between and , and the different-side structure means relations between where m, n are positive integers and T is a bounded linear operator on a Hilbert space. Thus, the original problem of powers of hyponormal operators belongs to different-side structure on powers of hyponormal operators. The structure on powers of p-hyponormal operators for p > 0 is emphasized. Also, some applications are obtained.      

A Real Analyticity Result for Symmetric Functions of the Eigenvalues of a Domain-Dependent Neumann Problem for the Laplace Operator

Let Ω be an open connected subset of for which the imbedding of the Sobolev space W ^1,2(Ω) into the space L ²(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset (Ω) of , where is a Lipschitz continuous homeomorphism of Ω onto (Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of . This paper represents an extension of a part of the work performed by P.D. Lamberti in his PhD Thesis at the University of Padova under the guidance of M. Lanza de Cristoforis.