bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solvability of boundary value problems for vector differential systems
Authors: Erbe L. H. , Liu Xinzhi , Wu Jianhong 
Published: November 2011

SynopsisBrouwer topological degree theory, the shooting type method, the disconjugacy theory of Hamiltonian systems and the Liapunov-Razumikhin technique of Volterra integrodifferential equations are employed to establish some solvability results for the 2n-dimensional differential systemsubject to one of the following boundary conditions:(i) x(0) = Qx(l), Qg(l x(1), qy(1)= g(0, x(0), y(0)),(ii) Blx(O) = B2g(O, x(O), y(O)), C1x(l) = −C2g(l, x(l), y(l)),where Q, Bi, Ci, i = 1, 2, are n x n real matrices. An application is given to the second order equation xn = h(t, x, x') subject to certain nonlinear boundary conditions.
Compact boundedness in periodic functional differential equations with infinite delay
Authors: Kato Junji 
Published: November 2011

SynopsisIt is the aim of this article to consider some problems arising from the non local-compactness of the phase space for functional differential equations. The compact boundedness, that is, the boundedness depending on each compact set involving the initial values, is proved to be implied from the ultimate boundedness for periodic systems of functional differential equations on Cγ: = {φ ∊ C((–∞,0]) Note that it is known that the compactness cannot be dropped in the above. An example is also given to show that the asymptotic stability is not necessarily uniform even for periodic functional differential equations on Co.
Lower semicontinuity of multiple integrals and the Biting Lemma
Authors: Ball J. M. , Zhang K.-W. 
Published: November 2011

SynopsisWeak lower semicontinuity theorems in the sense of Chacon's Biting Lemma are proved for multiple integrals of the calculus of variations. A general weak lower semicontinuity result is deduced for integrands which are acomposition of convex and quasiconvex functions. The “biting”weak limit of the corresponding integrands is characterised via the Young measure, and related to the weak* limit in the sense of measures. Finally, an example is given which shows that the Young measure corresponding to a general sequence of gradients may not have an integral representation of the type valid in the periodic case.
On the asymptotic decay of L2-solutions of one-body Schrödinger equations in unbounded domains
Authors: Hoffmann-Ostenhof M. 
Published: November 2011

SynopsisThe asymptotic decay of L2-solutions of Schrödinger equations (-Δ+V)ψ=0 in ΔR= {x εRn∣∣x∣=r>R} is investigated, where V(x) = V1(r) + V2(x) with V1→ ∞ for r↑∞ and with some ε > 0 for large r. Under additional assumptions on the decay of V1, pointwise upper bounds to |ψ |and lower bounds to the spherical average of ψ are given showing the same asymptotics for r→ ∞. For the case V→ const. > 0 for r→ ℝ (investigated in [8] a simplified treatment is given.
Corrigendum: Spectral properties of two parameter eigenvalue problems II
Authors: Binding Paul , Browne Patrick J. , Picard R. H. 
Published: November 2011

SynopsisThere are some mistakes in [1, Section 4], and since the main result, Theorem 4.4, is central to the theory and has already been applied in various contexts, we felt it advisable to give a complete statement and proof. The applications of vTheorem 4.4 made to date have fortunately been in situations where the results are correct. For convenience, we restate our notation.
A factorisation procedure for two by two matrix functions on the circle with two rationally independent entries
Authors: Prößdorf S. , Speck F.-O. 
Published: November 2011

SynopsisThe aim of this paper is the explicit canonical or standard factorisation of matrix functions with Wiener algebra elements. The present approach covers all regular 2 × 2 matrices where two entries are arbitrary and the remaining two are linear combinations of the former with rational coefficient functions. It is based on the knowledge of how to factorise scalar functions and rational matrix functions. In general, one also needs the approximation of any scalar Wiener algebra function with a rational function. However, this can be easily circumvented in many applications by intuitive manipulations with rational matrix functions.
On the Gegenbauer transformation
Authors: Heywood P. , Rooney P. G. 
Published: November 2011

SynopsisThe Gegenbauer transformation Gλk is defined for λ > −1/2, k = 0, 1, 2, …, bywhere, if being the Gegenbauer polynomial of index λ and degree k, and L0k is the Tchebichef polynomial of degree k. The transformation is studied on the spaces Lµ, p denned by the normand its boundedness and range on these spaces is determined and inversion formulae are found.
Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions
Authors: Budd C. , Knaap M. C. , Peletier L. A. 
Published: November 2011

SynopsisAsymptotic estimates are established for nontrivial positive radial eigenfunctions of the nonlinear eigenvalue problem −Δu= λ(up−uq) in the unit ballBin ℝN(N> 2) with Neumann boundary conditions, as the supremum norm tends to infinity. Herepis the critical Sobolev exponent (N+ 2)/(N− 2) and 0 <q<p− 1 = 4/(N− 2).
Normal structure coefficients of Lp(Ω)
Authors: Benavides T. Domínguez 
Published: November 2011

SynopsisLet X be a uniformly convex Banach space, and N(X) the normal structure coefficient of X. In this paper it is proved that N(X) can be calculated by considering only sets whose points are equidistant from their Chebyshev centre. This result is applied to prove that N(LP(Ω)) = min {21−1/p, 21/p}, Ω being a σ-finite measure space. The computation of N(Lp) lets us also calculate some other coefficients related to the normal structure.
Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs
Authors: Mrozek Marian , Rybakowski Krzysztof P. 
Published: November 2011

SynopsisConsider the semilinear evolution equation(P) u + Au = f(t,u)where A is a sectorial operator on a Banach space and f is ω-periodic in t. Using a time-discrete Conley index developed in a previous paper [6], we prove a few existence results on bounded solutions of (P) defined for all t ∊ R. More specific results are given for time-periodic scalar parabolic equations.
Schauder estimates and existence theory for entire solutions of linear elliptic equations
Authors: Begehr Heinrich , Hile G.N. 
Published: November 2011

SynopsisExistence as well as uniqueness theorems under certain growth conditions are given for entire solutions to linear elliptic equations in the n-dimensional space (2≦n). Introducing a proper norm, the proofs are based on a priori estimates. These estimates could be used to solve nonlinear equationsin the space, but the conditions on the nonlinearity have to be strong as the a priori estimates applyonly to classical, not to weak, solutions.
Some Borsuk-Ulam-type theorems for maps from Riemannian manifolds into manifolds
Authors: Hai-bao Duan 
Published: November 2011

SynopsisSuppose f: M →N is a continuous map from a Riemannian manifold (M, d) into a manifold N. The main result of this paper is to give some conditions under which f identifies a pair of cut points. This result leads to generalisations of the classical Borsuk-Ulam theorem. As a consequence some topological properties of locally symmetric spaces are discovered.
The gradient theory of phase transitions for systems with two potential wells
Authors: Fonseca Irene , Tartar Luc 
Published: November 2011

SynopsisIn this paper we generalise the gradient theory of phase transitions to the vector valued case. We consider the family of perturbationsof the nonconvex functionalwhere W:RN→R supports two phases and N ≧1. We obtain the Γ(L1(Ω))-limit of the sequenceMoreover, we improve a compactness result ensuring the existence of a subsequence of minimisers of Eε(·) converging in L1(Ω) to a minimiser of E0(·) with minimal interfacial area.
An antiradical for near-rings
Authors: Hartney J. F. T. 
Published: November 2011

SynopsisThroughout this article, the near-ring N is assumed to be zero symmetric and to satisfy the right distributive law. We construct an ideal called the socle-ideal of N which is antiradical in the sense that it is a direct sum of minimal left ideals and annihilates one or more of the radicals of N. We then use this socle-ideal to obtain a decomposition theorem for the s-radical JS(N) of N.
On some properties of matrices associated with linear ordinary quasi-differential expressions
Authors: Everitt W. N. , Key Jennifer D. 
Published: November 2011

SynopsisIn the general theory of ordinary linear quasi-differential equations, the set of Shin–Zettl matrices plays an important role. This paper displays certain properties of these matrices and their behaviour under a special form of transformation. Essentially, the problems can be considered within the framework of linear algebra.
Multiplicity results for a nonlinear Dirichlet problem
Authors: Solimini S. 
Published: November 2011

SynopsisThis paper deals with some multiplicity results for elliptic problems with jumping nonlinearities. Our results are concerned with the case in which only one eigenvalue of the linear problem is jumped and it is simple. The main tool used is the Leray–Schauder topological degree. We consider a parametrized problem and prove the existence of two or three distinct solutions for suitable values of the parameter.
Monogenic inverse semigroups and their C* -algebras
Authors: Conway J. B. , Duncan J. , Paterson A. L. T. 
Published: November 2011

SynopsisBy using the Halmos-Wallen description of power partial isometries on Hilbert space, we give a complete description of all monogenic inverse semigroups,ℐ. We also describe the fullC*-algebraC*ℐand the reducedC*-algebra C*(ℐ)with particular emphasis on the case of the free monogenic inverse semigroupℑℐt.
Memory effect phenomena and Г-convergence
Authors: Mascarenhas Maria Luisa 
Published: November 2011

SynopsisIt is known that the parametric equation u'∊+ a∊u∊ = f, u∊ (0)= 0,with α ≦ a∊ ≦ β, for all ∊ > 0 and almost everywhere in a bounded domain Ω of ℝN, and f in L∞((0, T) × Ω), shows, at the limit, a memory effect. In this work the associated minimisation problem is considered and we describe how the memory effect appears in the Γ-limit, for the weak topology H1:(0, T; L2(Ω)) of the corresponding functional. The sequence a∊ has no dependence in time.
Exact controllability for a model of a multidimensional flexible structure
Authors: Puel Jean Pierre , Zuazua Enrique 
Published: November 2011

SynopsisA simple model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional straight string is introduced. In both regions (n-dimensional body and a onedimensional string) the state is assumed to satisfy the wave equation. Simple boundary conditions are introduced at the junction. These conditions, in the absence of control, ensure conservation of the total energy of the system and imply some rigidity of the boundary of the n-d body on a neighbourhood of the junction. The exact boundary controllability of the system is proved by means of a Dirichlet control supported on a subset of the boundary of the n-d domain which excludes the junction region. Some extensions are discussed at the end of the paper.
On the equation ut = ∆uα + uβ
Authors: Qi Yuan-Wei 
Published: November 2011

SynopsisThe Cauchy problem of ut, = ∆uα + uβ, where 0 < α < l and α>1, is studied. It is proved that if 1< β<α + 2/n then every nontrivial non-negative solution is not global in time. But if β>α+ 2/n there exist both blow-up solutions and global positive solutions which decay to zero as t–1/(β–1) when t →∞. Thus the famous Fujita result on ut = ∆u + up is generalised to the present fast diffusion equation. Furthermore, regarding the equation as an infinite dimensional dynamical system on Sobolev space W1,s (W2.s) with S > 1, a non-uniqueness result is established which shows that there exists a positive solution u(x, t) with u(., t) → 0 in W1.s (W2.s) as t → 0.
The distribution of genera among quadratic spaces over global fields
Authors: Earnest A. G. 
Published: November 2011

SynopsisFor a Hasse domain R in a global field F, the distribution of genera of R-lattices with specified invariants among the nonisometric quadratic spaces over F which contain them is studied. It is shown that such genera are equally distributed for spaces of dimension 2, but that this is not generally the case for spaces of dimension exceeding 2. Theresult in the binary case yields an extension of a dimension exceeding 2. The result in the binary case yields an extension of a theorem of Gauss.
The G-closure of two well-ordered, anisotropic conductors
Authors: Grabovsky Yury 
Published: November 2011

SynopsisWe give a complete solution to the G-closure problem for mixtures of two well-ordered possibly anisotropic conductors. Both the G-closure with fixed volume fractions and the full G-closure are computed. The conductivity tensors are considered in a fixed frame and no rotations are allowed.
Nonlinear dynamical theory of the elastica
Authors: Caflisch Russel E. , Maddocks John H. 
Published: November 2011

SynopsisThe dynamical behaviour of a slender rod is analyzed here in terms of a generalization of Euler's elastica theory. The model includes a linear stress-strain relation but nonlinear geometric terms. Properties of the rod may vary along its length and various boundary conditions are considered. A rotational inertia term that is neglected in many theories is retained, and is essential to the analysis. By use of the equivalence of an energy and a Sobolev norm, and by reformulation of the equations as a semilinear system, global existence of solutions is proved for any smooth initial data. Equilibrium solutions that are stable in the static sense of minimizing the potential energy are then proved to be stable in the dynamic sense due to Liapounov.
Boundary value conditions for wave fronts in reaction-diffusion systems
Authors: Fraile J. M. , Sabina J. 
Published: November 2011

SynopsisIn this paper, we introduce a new class of solutions of reaction-diffusion systems, termed directional wave front solutions. They have a propagating character and the propagation direction selects some distinguished boundary points on which we can impose boundary conditions. The Neumann and Dirichlet problems on these points are treated here in order to prove some theorems on the existence of directional wave front solutions of small amplitude, and to partially establish their asymptotic behaviour.
K-analytic uniform structures
Authors: Canela Miguel A. 
Published: November 2011

SynopsisThis article deals with the uniform spaces (X, μ) such that μ is a K-analytic subset of 2X×X. G. Godefroy considered this situation for X countable, in his study of certain compact sets of measurable functions, and some of his results are extended here. We prove that the uniformity of an Eberlein compact is K-analytic, and give some applications.
Balanced big Cohen-Macaulay modules and ring extensions
Authors: O'Carroll Liam 
Published: November 2011

SynopsisLet A and B be commutative Noetherian local rings such that B contains A and B is flat and integral over A. It is shown that if M is a balanced big Cohen-Macaulay A-module (that is, every system of parameters for A is an M-sequence), then M⊗AB is a balanced big Cohen-Macaulay B-module. An example of a ring A is given such that, if B is the completion of A, then the analogous result is false in this case. This answers a question posed by Riley in the negative.
Asymptotic solutions to linear differential equations with coefficients of the power order of growth, 2
Authors: Lantsman M. H. 
Published: November 2011

SynopsisWe consider linear differential equations of the form F(x, z)≡ xn + a1(z)x(n-1)+…+an(z)x = 0 with power-logarithmic coefficients or coefficients which are asymptotically similar to power-logarithmic functions in a central sector S of a complex plane for z →∞, z∈S. The main result of this paper is that in a sufficiently small central sector SE⊂S there is a fundamental system of solutions {xi(z) = exp [∫γi(z)dz)} where each function γi(z) is equivalent to a power-logarithmic function or has an estimate of the form O(z−∞). Furthermore, a precise estimate is obtained for a partial solution of a nonhomogeneous equation F(x, z) = α(z), where the function α(z) grows like a power.
The extreme points of some classes of polynomials
Authors: Brannan D. A. , Clunie J. G. 
Published: November 2011

SynopsisWe study the extreme points of two classes of polynomials of degree at most n:It turns out that f ∈ Ext if and only if Re f(eiθ) has exactly 2n zeros in [0, 2π). On the other hand, if f∈Hn and 1−|f(eiθ)|2 has 2n zeros in [0, 2π), then either f ∈ Ext Hn or else f(z) = α + βzn where |α|+|β| = l and αβ≠0; if 1−|f(eiθ)|2 has 2m zeros, 2n, then f may or may not belong to Ext Hn.
On an inequality of Hardy-Littlewood type: I
Authors: Evans W. D. , Everitt W. N. 
Published: November 2011

SynopsisThis paper gives a complete analysis of the integral inequalitywhere the integral on the left may be only conditionally convergent. It is shown that the best possible number K is 4 and all cases of equality are identified in terms of Hankel-Bessel functions of order ⅓.
On the existence of periodic solutions for autonomous retarded functional differential equations on R2
Authors: Dos Reis J. G. , Baroni R. L. S. 
Published: November 2011

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.
Remarks on the quasi-steady one phase Stefan problem
Authors: Louro Bento , Rodrigues José-Francisco 
Published: November 2011

SynopsisThis paper presents some regularity results on the solution and on the free boundary for the one phase Stefan problem with zero specific heat in the framework of the variational inequalities formulation. In particular we show the Hölder continuity of the free boundary. Estimates on the rate of convergence when the specific heat vanishes are given for the variational solutions and for the free boundaries.
Linearisation at infinity and Lipschitz estimates for certain problems in the calculus of variations
Authors: Chipot Michel , Evans Lawrence C. 
Published: November 2011

SynopsisWe demonstrate local Lipschitz regularity for minimisers of certain functionals which are appropriately convex and quadratic near infinity. The proof employs a blow-up argument entailing a linearisation of the Euler—Lagrange equations “at infinity”. As a application, we prove that minimisers for the relaxed optimal design problem derived by Kohn and Strang [3] are locally Lipschitz.
An expansion theory for non-self-adjoint boundary-value problems
Authors: Walker Philip W. 
Published: November 2011

SynopsisThis paper deals with two-point boundary-value problems for ordinary differential equations and the operators which they induce in the appropriate Hilbert space. The problems arenot required to be self-adjoint. No auxiliary condition such as Birkhoff-regularity is imposed. If T is such an operator, it may well have no meaningful spectral structure. It is shown, however, that when T is composed with its adjoint, the result is a non-negative self-adjoint differential operator. The eigenvalues and eigenfunctions of this composite operator are used to delineate the domain, action, range, and generalised inverse of T.
Uniqueness and non-uniqueness of normal forms for vector fields
Authors: Baider Alberto , Churchill Richard 
Published: November 2011

SynopsisThe use of normal forms in the study of equilibria of vector fields and Hamiltonian systems is a well-established practice and is described in standard references (e.g. [1], [7] or [10]). Also well known is the fact that such normal forms are not unique, and the relationship between distinct normal forms of the same vector field has also been investigated, in particular by M. Kummer [8] and A. Brjuno [2,3] (also see [12]). In this paper we use this relationship to extract invariants of the vector field directly from an arbitrary normal form. The treatment is sufficiently general to handle the vector field and Hamiltonian cases simultaneously, and applications in these contexts are presented.The formulation of our main result (Theorem 1.1) is reminiscent of, and was heavily influenced by, work of Shi Songling on planar vector fields [11]. Additional inspiration was provided by M. Kummer's contributions to the 1:1 resonance problem in [9]. The authors are grateful to Richard Cushman for comments on an earlier version of this paper.
The change in index of a graph resulting from the attachment of a pendant edge
Authors: Bell F. K. , Rowlinson P. 
Published: November 2011

SynopsisConditions are obtained under which a graph G', obtained from a graph G by the attachment of a pendant edge, may be regarded as a perturbation of G. In this situation the index of G' is expressed as the sum of a convergent series whose terms are determined by the spectrum and certain angles of G.
Polynomial interpolation at points of a geometric mesh on a triangle
Authors: Lee S. L. , Phillips G. M. 
Published: November 2011

SynopsisIn an earlier paper [8], I. J. Schoenberg discussed polynomial interpolation in one dimension at the points of a geometric progression, which was originally proposed by James Stirling. In the present paper, these ideas are generalised to two-dimensional polynomial interpolation at the points of a geometric mesh on a triangle. A Lagrange form is obtained for this interpolating polynomial and an algorithm is derived for evaluating it efficiently.
The critical Sobolev exponent in two dimensions
Authors: McLeod Bryce , McLeod Kevin 
Published: November 2011

SynopsisThe object of the paper is to investigate solutions of equations of the formwithand in particular to look at the asymptotic behaviour of these solutions as γ ↑∞. It is found that, if tγ is the first zero of ϑ, thenwhile tγ is bounded below if p < 2. This answers questions raised by Brezis concerning solutions of −Δu = eup in R2
A perturbation result of semilinear elliptic equations in exterior strip domains
Authors: Hsu Tsing-san , Wang Hwai-chiuan 
Published: November 2011

SynopsisIn this paper we show that if the decay of nonzero ƒ is fast enough, then the perturbation Dirichlet problem−Δu + u = up+ ƒ(z)in Ω has at least two positive solutions, wherea boundedC1,1domainS= × ωRn, Dis a boundedC1,1domain inRm+nsuch thatD ⊂⊂ Sand Ω = S\D. In case ƒ ≡ 0, we assert that there is a positive higher-energy solution providing thatDis small.
The spectrum and eigenspaces of a meromorphic operator-valued function
Authors: Magnus Robert 
Published: November 2011

SynopsisIt is shown how to associate eigenvectors with a meromorphic mapping defined on a Riemann surface with values in the algebra of bounded operators on a Banach space. This generalises the case of classical spectral theory of a single operator. The consequences of the definition of the eigenvectors are examined in detail. A theorem is obtained which asserts the completeness of the eigenvectors whenever the Riemann surface is compact. Two technical tools are discussed in detail: Cauchy-kernels and Runge's Approximation Theorem for vector-valued functions.
Renormalised solutions of nonlinear parabolic problems with L1 data: existence and uniqueness
Authors: Blanchard D. , Murat F. 
Published: November 2011

In this paper we prove the existence and uniqueness of a renormalised solution of the nonlinear problemwhere the data f and u0 belong to L1(Ω × (0, T)) and L1 (Ω), and where the function a:(0, T) × Ω × ℝN → ℝN is monotone (but not necessarily strictly monotone) and defines a bounded coercive continuous operator from the space into its dual space. The renormalised solution is an element of C0 ([ 0, T] L1 (Ω)) such that its truncates TK(u) belong to withthis solution satisfies the equation formally obtained by using in the equation the test function S(u)φ, where φ belongs to and where S belongs to C∞(ℝ) with