bluuebunny/crossref_metadata_2025_split huggingface dataset:
Diffusive logistic equations with indefinite weights: population models in disrupted environments
Authors: Cantrell Robert Stephen , Cosner Chris 
Published: November 2011

SynopsisThe dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form ut = d Δu + [m(x) — cu]u in Ω × (0, ∞), where u represents the population density, c, d > 0 are constants describing the limiting effects of crowding and the diffusion rate of the population, respectively, and m(x) describes the local growth rate of the population. If the environment ∞ is bounded and is surrounded by uninhabitable regions, then u = 0 on ∂∞× (0, ∞). The growth rate m(x) is positive on favourablehabitats and negative on unfavourable ones. The object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled. The models are shown to possess a unique, stable, positive steady state (implying persistence for the population) provided l/d> where is the principle positive eigenvalue for the problem — Δϕ=λm(x)ϕ in Χ,ϕ=0 on ∂Ω. Analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat. In the limit as the diffusion rate d ↓ 0, the solutions tend toward the positive part of m(x)/c, and if m is discontinuous develop interior transition layers. The analysis uses bifurcation and continuation methods, the variational characterisation of eigenvalues, upper and lower solution techniques, and singular perturbation theory.
Exact estimates of the conductivity of a binary mixture of isotropic materials
Authors: Lurie K. A. , Cherkaev A. V. 
Published: November 2011

SynopsisThis paper describes the set GmU of effective conductivity tensors of mixtures generated by two isotropic materials taken in prescribed proportions m1 and m2 We describe microstructures which realise any point of GmU for n-dimensional space.
The Ljapunov equation and an application to stabilisation of one-dimensional diffusion equations
Authors: Nambu Takao 
Published: November 2011

SynopsisA Ljapunov equationXL − BX = Cappears in stabilisation studies of linear systems. Here, the operatorsL, B, andCare given linear operators working in infinite-dimensional Hilbert spaces, which are derived from a specific control system. We have so far considered the case whereLis a general elliptic operator of order 2 in a bounded domain of an Euclidean space. WhenLis instead a self-adjoint elliptic operator working in an interval of ℝ1, we derive here a stronger geometrical character of the solutionXto the Ljapunov equation. The result is applied to stabilisation of one-dimensional diffusion equations.
Left approximate identities in algebras of compact operators on Banach spaces
Authors: Dixon P. G. 
Published: November 2011

SynopsisWe study the existence of left approximate units, left approximate identities and bounded left approximate identities in the algebras (X)of all compact operators on a Banach space X and ℱ(X)− of all operators uniformly approximable by finite rank operators. In the case of bounded left approximate identities, necessary and sufficient conditions on X are obtained. In the other cases, sufficient conditions are obtained, together with an example of non-existence using a space constructed by Szankowski. The possibility of the sufficient conditions being also necessary depends on the question of whether every compact set is contained in the closure of the image of the unit ball under an operator in (X)(or ℱ(X)−). Sufficient conditions on X are obtained for this to be true, but it is conjectured that the answer for general X is negative.
On a gradient-like integro-differential equation
Authors: Hale Jack K. , Rybakowski Krzysztof P. 
Published: November 2011

SynopsisUnder appropriate conditions on b and a function g with 2k +1 simple zeros, the equationhas a maximal compact invariant set Ab,g in C([−1,0]R), consisting of the zeros of g and the one-dimensional unstable manifolds of these zeros. For k =2, it is shown that there may be a saddle connection in the flow on Ab,g for some g. This implies that the zeros of g as elements of the flow on Ab,g cannot be given the natural order of the reals.
On the boundary value problems of electro- and magnetostatics
Authors: Picard Rainer 
Published: November 2011

SynopsisThe classically well-known relation between the number of linearly independent solutions of the electro- and magnetostatic boundary value problems (harmonic Dirichlet and Neumann vector fields) and topological characteristics (genus and number of boundaries) of the underlying domain in 3-dimensional euclidean space is investigated in the framework of Hilbert space theory. It can be shown that this connection is still valid for a large class of domains with not necessarily smooth boundaries (segment property). As an application the inhomogeneous boundary value problems of electro- and magnetostatics are discussed.
Hermite–Birkhoff interpolation by Hermite–Birkhoff splines
Authors: Goodman T. N. T. 
Published: November 2011

SynopsisWe consider interpolation by piecewise polynomials, where the interpolation conditions are on certain derivatives of the function at certain points, specified by a finite incidence matrix E. Similarly the allowable discontinuities of the piecewise polynomials are specified by a finite incidence matrix F. We first find necessary conditions on (E, F) for the problem to be poised, that is to have a unique solution for any given data. The main result gives sufficient conditions on (E, F) for the problem to be poised, generalising a well-known result of Atkinson and Sharma. To this end we prove some results involving estimates of the numbers of zeros of the relevant piecewise polynomials.
Existence of conjugate points for second and fourth order differential equations
Authors: Müller-Pfeiffer E. 
Published: November 2011

SynopsisThe paper presents sufficient conditions on the coefficients of second and fourth order differential equations to ensure that there exists at least one pair of conjugate points on an interval (a, b), −∞≦ a <b ≦ ∞. Oscillation criteria related to the equation (p(x)y″)″ + q(x)y = 0, 0 < x < ∞, are proved with no sign restrictions on q(x).
Non-existence of eigenvalues of Dirac operators
Authors: Kalf Hubert 
Published: November 2011

SynopsisAbsence of non-trivial square integrable solutions of the Dirac equationfor values of λ in half-rays is proved under local conditions on q, curl b, and the radial derivative of q. The Coulomb potential is admitted. Another result does not contain any growth condition on the radial derivative of q. It states that there are no solutions of integrable square other than the trivial solution if λ ε ℝ\ [−1, 1] and
Oscillatory and asymptotic properties of a class of operator-differential inequalities
Authors: Myshkis A. D. , Bainov D. D. , Zahariev A. I. 
Published: November 2011

SynopsisThe present paper studies some asymptotic (including oscillatory) properties of the solutions of operator-differential inequalities of the formwhere(the latter symbol denotes the space of locally summable functions).As an application of the results obtained, theorems are proved for the asymptotic behaviour of the solutions of certain classes of functional-differential and integro-differential neutral-type equations.
Associated Laguerre and Hermite polynomials
Authors: Askey Richard , Wimp Jet 
Published: November 2011

SynopsisExplicit orthogonality relations are found for the associated Laguerre and Hermite polynomials. One consequence is the construction of the [n − 1/n] Padé approximation to Ψ(a + 1, b; x)/Ψ(a, b; x), where Ψ(a, b; x) is the second solution to the confluent hypergeometric differential equation that does not grow rapidly at infinity.
Semicontinuous envelopes of polyconvex integrals
Authors: Acerbi Emilio , Buttazzo Giuseppe 
Published: November 2011

SynopsisWe answer some questions about the semicontinuity inL∞and inLpof functionals defined onW1,n(Ωℝn) as integrals of non-convex functions of the gradient matrix, and we give a conjecture for the general case.
On the traction problem for linear elastostatics in exterior domains
Authors: Padula Mariarosaria 
Published: November 2011

SynopsisIn this note, we study the well-posedness of the exterior traction value problem for linear anisotropic non-homogeneous elastostatics. We prove existence and continuous dependence upon the data. In particular, in the isotropic homogeneous case, provided the body force is “simple”, we show that solutions tend to zero uniformly at large spatial distances.
Doubly-null-concordant simple even-dimensional knots
Authors: Kearton C. 
Published: November 2011

SynopsisThe simple 2q-knots, q ≧ 5, for which contains no ℤ-torsion, have been classified in terms of Hermitian duality pairings on their homology and homotopy modules. In this paper, a necessary and sufficient condition is given for such a knot to be doubly-null-concordant.
The deficiency indices of powers of second order expressions with large leading coefficient
Authors: Read Thomas T. 
Published: November 2011

SynopsisThe deficiency index of each power of the differential expression M[y] = w−1(−(py′)′ + qy), defined on [a, ∞), is calculated exactly in terms of the behaviour of a simple function of p and w for a large class of expressions satisfying a hypothesis which requires that p be large compared with w and q. In general, not all powers of M are limit-point.
On Malcev algebras in which all subideals are ideals
Authors: Elduque Alberto 
Published: November 2011

SynopsisMalcev algebras in which the relation of being an ideal is transitive are studied as well as those Malcev algebras in which every subalgebra satisfies that condition. These algebras are closely related to those in which right multiplication by any element is semisimple and they are used to determine Malcev algebras with a relatively complemented lattice of subalgebras.
The group of homotopy self-equivalences of non-simply-connected spaces using Postnikov decompositions II
Authors: Rutter John W. 
Published: November 2011

SynopsisWe give here an abelian kernel (central) group extension sequence for calculating, for a non-simply-connected space X, the group of pointed self-homotopy-equivalence classes . This group extension sequence gives in terms of , where Xn is the nth stage of a Postnikov decomposition, and, in particular, determines up to extension for non-simplyconnected spaces X having at most two non-trivial homotopy groups in dimensions 1 and n. We give a simple geometric proof that the sequence splits in the case where is the generalised Eilenberg–McLane space corresponding to the action ϕ: π1 → aut πn, and give some information about the class of the extension in the general case.
Existence and boundedness of a minimiser for a constrained minimisation problem on Rn with limiting exponent
Authors: Yaotian Shen , Shusen Yan 
Published: November 2011

SynopsisWe use the concentration compactness principle to study the existence of a minimiser of the minimisation problem where u =(u1, …, uN), . We also prove the boundedness of the minimiser of l1 by using the reverse Holder inequality.
Convergence in Lotka–Volterra-type delay systems without instantaneous feedbacks
Authors: Kuang Yang , Smith Hal L. 
Published: November 2011

SynopsisMost of the convergence results appearing so far for delayed Lotka–Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka–Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.
An example of H1-unboundedness of solutions to strongly elliptic systems of partial differential equations in a laminated geometry
Authors: Le Dret Hervé 
Published: November 2011

SynopsisIn this paper, a counterexample is given to the H1-boundedness of solutions to a sequence of systems of linear partial differential equations uniformly satisfying a strict Legendre–Hadamard condition and whose coefficients depend on one direction only. This counterexample is relevant for the theory of homogenisation of laminated elastic materials.
Trend to spatial homogeneity for solutions to semilinear damped wave equations
Authors: Solà-Morales J. , València M. 
Published: November 2011

SynopsisThe semilinear damped wave equationssubject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.
Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains
Authors: Fortunato Donato , Jannelli Enrico 
Published: November 2011

SynopsisWe consider the boundary value problemwhere Ω ⊂ ℝn is a bounded domain, n≧3, 2* = 2n/(n − 2) is the critical exponent for the Sobolev embedding and λ is a real positive parameter. We prove the existence of infinitely many solutions of (*) when Ω exhibits suitable symmetries.
A Laplace transform relevant to holomorphic semigroups
Authors: Rebarber R.L. 
Published: November 2011

SynopsisA Laplace transform is developed for functions which are holomorphic in the complex wedge Ω = {z| |arg (z)| < σ}, where 0 ≦ σ < π. The resulting transform will be holomorphic in a complementary wedge of the form Ωa = {a+ z||arg (z)|< (π/2) +σ for some a. This Laplace transform is shown to be an isomorphism between two appropriate spaces. The spanning properties of sets of the form {eλkS}k∊I in the domain space are studied. These results are then applied to a control problem.
Radial entire solutions to even order semilinear elliptic equations in the plane
Authors: Kusano Takaŝi , Naito Manabu , Swanson Charles A. 
Published: November 2011

SynopsisSemilinear elliptic equations of the formare considered, where Δm is the m-th iterate of the two-dimensional Laplacian Δ, p(t) is continuous in [0, ∞), and f(u is continuous and positive either in (0, ∞) or in ℝ.Our main objective is to present conditions on p and f which imply the existence of radial entire solutions to (*), that is, those functions of class C2m(ℝ2) which depend only on |x| and satisfy (*) pointwise in ℝ2.First, necessary and sufficient conditions are established for equation (*), with p(t) > 0 in [0, ∞), to possess infinitely many positive radial entire solutions which are asymptotic to positive constant multiples of |x|2m−2 log |x as |x| → ∞. Secondly, it is shown that, in the case p(t < 0, in [ 0, ∞) and f(u) > 0 is nondecreasing in ℝ, equation (*) always has eventually negative radial entire solutions, all of which decrease at least as fast as negative constant multiples of |x|2m−2 log |x| as |x| → ∞. Our results seem to be new even when specialised to the prototypeswhere γ is a constant.
An analytical study of bifurcation problems for equations involving Fredholm mappings
Authors: Tan N.X. 
Published: November 2011

Let us consider equations in the formwhere Λ is an open subset of a normed space. For any fixed λ ∊ Λ, T, L(λ,.) and M(λ,.) are mappings from the closure D0 of a neighbourhood D0 of the origin in a Banach space X into another Banach space Y with T(0) = L(λ, 0) = M(λ, 0) = 0. Let λ be a characteristic value of the pair (T, L) such that T − L(λ,.) is a Fredholm mapping with nullity p and index s, p> s≧ 0. Under sufficient hypotheses on T, L and M, (λ, 0) is a bifurcation point of the above equations. Some well-known results obtained by Crandall and Rabinowitz [2], McLeod and Sattinger [5] and others will be generalised. The results in this paper are extensions of the results obtained by the author in [7].
Stochastic generalised KPP equations
Authors: Davies I. M. , Truman A. , Zhao H. Z. 
Published: November 2011

We classify multiplicative white noise perturbationsk(·)dw, of generalised KPP equations and their effects on deterministic approximate travelling wave solutions by the behaviour of, the solutions of the stochastic generalised KPP equations converge to deterministic approximate travelling waves and ifbeing an associated potential energy, Фsa solution of the corresponding classical mechanical equations of Newton,Dbeing a certain domain inR1×Rrthen the white noise perturbations essentially destroy the wave structure and force the solutions to die down.For the case(suppose the existence of the limit) we show that there is a residual wave form but propagating at a different speed from that of the unperturbed equations. Numerical solutions are included and give good agreement with theoretical results.
Existence and uniqueness of the global admissible solution for a viscoelastic model with relaxation
Authors: Zhao Huijiang 
Published: November 2011

This paper examines the Cauchy problem for a viscoelastic model with relaxationwith discontinuous, large initial data, where ½ ≦ μ <1, δ > 0 are constants. We first give a definition of admissible (or entropic) solutions to the system. Under this definition, we prove the existence, uniqueness and continuous dependence of the global admissible solution for the system. Our methods are essentially due to Kruzkov, and the requirement that f(u) is not badly degenerate (more precisely, meas {x: f″(x) = 0} = 0), needed previously when considering the global existence problem for the same system, is removed.
Unique continuation properties of the nonlinear Schrödinger equation
Authors: Zhang Bing-Yu 
Published: November 2011

Consider the unique continuation problem for the nonlinear Schrödinger (NLS) equationBy using the inverse scattering transform and some results from the Hardy function theory, we prove that if u ∈ C(R; H1(R)) is a solution of the NLS equation, then it cannot have compact support at two different moments unless it vanishes identically. In addition, it is shown under certain conditions that if u is a solution of the NLS equation, then u vanishes identically if it vanishes on two horizontal half lines in the x–t space. This implies that the solution u must vanish everywhere if it vanishes in an open subset in the x–t space.
Dynamic boundary conditions for the Navier–Stokes equations
Authors: Grobbelaar-Van Dalsen Maríe , Sauer Niko 
Published: November 2011

SynopsisWhen a symmetric rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. These equations at the boundary contain a time derivative and thus are of a dynamic nature. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity and pressure fields of the fluid motion and the angular velocity of the rigid body.In this paper we formulate the physical problem for the case of rotation about an axis of symmetry as an abstract ordinary differential equation in two Banach spaces in which the velocity field is the only unknown. To achieve this, a method for the elimination of the pressure field, which also occurs in the boundary condition, is developed. Existence and uniqueness results for the abstract equation are derived with the aid of the theory of B-evolutions and the associated theory of fractional powers of a closed pair of operators.
Evolution equations with dynamic boundary conditions
Authors: Hintermann Thomas 
Published: November 2011

SynopsisIn this paper, we study boundary problems with dynamic boundary conditions, that is, with boundary operators containing time derivatives. The equations under consideration are transformed into abstract Cauchy problems x – Cx = f and x(0) = x0. Abstract theoretical results concerning the operators C are obtained by the study of a naturally arising pseudodifferential operator. For existence and uniqueness theorems concerning solutions of parabolic and hyperbolic equations, we then apply the theory of semigroups in Banach spaces. Some examples of semilinear and quasilinear problems, to which our results apply, are given.
On the existence of weak solutions for a nonlinear time dependent Dirac equation
Authors: Dias João-Paulo , Figueira Mário 
Published: November 2011

SynopsisIn this paper we prove the existence of a weak solution of the Cauchy problem for the nonlinear Dirac equation in ℝ × ℝwhere X(r) is the characteristic function of a compact interval of ]0, + ∞[
Wright's equation has no solutions of period four
Authors: Nussbaum Roger D. 
Published: November 2011

SynopsisLetN:ℝ→ℝ be a locally Lipschitzian map such that (y+ l)N(y)>0 for ally≠ –1 and such thatN(y)=1 +yfor – 1 ≦y≦ 3. For any positive number α the equationy'(t) αy(t–1)N(y(t)) has, aside from the constantsolutionsy(t) ≡ –1, andy(t) ≡–1 solutiony(t) such thaty(t+ 4) =y(t) for all realtIfN(y) = 1 +yfor ally, one obtains Wright's equation, which isknown to have periodic solutions of minimal periodp(depending on α) arbitrarily close to 4. Some results concerning nonexistence of periodic solutions of period 4 of other differential-delay equations are also proved. In all cases the method of proof consists in analysing an associated fourth-order system of ordinary differential equationsand showing that this system has no nonconstant periodic solutions.
Periodic solutions of a class of Hamiltonian systems with singularities
Authors: Ambrosetti Antonio , Ekeland Ivar 
Published: November 2011

SynopsisThis paper deals with a class of time-periodic Hamiltonian systems obtained by a time-dependent perturbation from an autonomous system with a singularity at q = 0 in configuration space. It is shown that, T being the period of the perturbation, nondegenerate families of T-periodic orbits in the unperturbed problem branch off into a certain number of T-periodic orbits for the perturbed problem.
Some examples of rank one convex functions in dimension two
Authors: Dacorogna B. , Douchet J. , Gangbo W. , Rappaz J. 
Published: November 2011

SynopsisWe study the rank one convexity of some functionsf(ξ) where ξ is a 2 × 2 matrix. Examples such as |ξ|2α+h(detξ) and | ξ |2α(| ξ |2− γdet ξ) are investigated. Numerical computations are done on the example of Dacorogna and Marcellini,indicating that this function is quasiconvex.
A dynamical systems proof of the Krein–Rutman Theorem and an extension of the Perron Theorem
Authors: Alikakos Nicholas D. , Fusco Giorgio 
Published: November 2011

SynopsisIn this paper we establish Perron and Krein–Rutman-like theorems for an operator mapping a cone into the interior of the cone, by considering the discrete dynamical system for the induced operator on the projective space (= sphere). Existence of a positive eigenvector reduces to showing that the ω-limit set of the induced operator consists of a single equilibrium. A special feature of our approach is that the convexity of the cone is needed only for establishing the non-emptiness of the w-limit set. This allows us in finite dimensions to establish an abstract Perron Theorem for non-convex cones.