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1.
In this paper, we will give some optimal estimates on the rotation number of the linear equation
and that of the asymmetric equation:
where p(t) and q(t) are almost periodic functions and
These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions.
Supported by the National Natural Science Foundation of China (no. 10325102), TRAPOYT-M.O.E. of China (2001), and the National
973 Project of China (no. G1999075108).
Received: April 6, 2004; revised: July 7, 2004 相似文献
2.
A regular extension phenomenon of functions defined on Euclidean space with values in a Clifford algebra was studied by Le
Hung Son in the 90’s using methods of Clifford analysis, a function theory which, is centred around the notion of a monogenic
function, i.e. a null solution of the firstorder, vector-valued Dirac operator in .
The isotonic Clifford analysis is a refinement of the latter, which arises for even dimension. As such it also may be regarded
as an elegant generalization to complex Clifford algebra-valued functions of both holomorphic functions of several complex
variables and two-sided biregular function theories.
The aim of this article is to present a Hartogs theorem on isotonic extendability of functions on a suitable domain of . As an application, the extension problem for holomorphic functions and so for the two-sided biregular ones is discussed.
相似文献
3.
In this paper we use Rab’s lemma [M. Ráb, Über lineare perturbationen eines systems von linearen differentialgleichungen, Czechoslovak Math. J. 83 (1958) 222–229; M. Ráb, Note sur les formules asymptotiques pour les solutions d’un systéme d’équations différentielles linéaires, Czechoslovak Math. J. 91 (1966) 127–129] to obtain new sufficient conditions for the asymptotic equivalence of linear and quasilinear systems of ordinary differential equations. Yakubovich’s result [V.V. Nemytskii, V.V. Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, New Jersey, 1966; V.A. Yakubovich, On the asymptotic behavior of systems of differential equations, Mat. Sb. 28 (1951) 217–240] on the asymptotic equivalence of a linear and a quasilinear system is developed. On the basis of the equivalence, the existence of asymptotically almost periodic solutions of the systems is investigated. The definitions of biasymptotic equivalence for the equations and biasymptotically almost periodic solutions are introduced. Theorems on the sufficient conditions for the systems to be biasymptotically equivalent and for the existence of biasymptotically almost periodic solutions are obtained. Appropriate examples are constructed. 相似文献
4.
H. Bereketoglu 《Periodica Mathematica Hungarica》1992,24(1):13-22
The aim of this paper is to investigate sufficient conditions (Theorem 1) for the nonexistence of nontrivial periodic solutions
of equation (1.1) withp ≡ 0 and (Theorem 2) for the existence of periodic solutions of equation (1.1). 相似文献
5.
Summary We obtain sufficient conditions for the existence of almost periodic weak solutions to equations of the frictionless pendulum type with forcing. 相似文献
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7.
Alan Dow 《Topology and its Applications》2010,157(8):1379-1857
We consider generalizations of a well-known class of spaces, called by S. Mrówka, N∪R, where R is an infinite maximal almost disjoint family (MADF) of countable subsets of the natural numbers N. We denote these generalizations by ψ=ψ(κ,R) for κ?ω. Mrówka proved the interesting theorem that there exists an R such that |βψ(ω,R)?ψ(ω,R)|=1. In other words there is a unique free z-ultrafilter p0 on the space ψ. We extend this result of Mrówka to uncountable cardinals. We show that for κ?c, Mrówka's MADF R can be used to produce a MADF M⊂ω[κ] such that |βψ(κ,M)?ψ(κ,M)|=1. For κ>c, and every M⊂ω[κ], it is always the case that |βψ(κ,M)?ψ(κ,M)|≠1, yet there exists a special free z-ultrafilter p on ψ(κ,M) retaining some of the properties of p0. In particular both p and p0 have a clopen local base in βψ (although βψ(κ,M) need not be zero-dimensional). A result for κ>c, that does not apply to p0, is that for certain κ>c, p is a P-point in βψ. 相似文献
8.
Bifurcation of fixed points from a manifold of trivial fixed points in the infinite-dimensional case
Massimo Furi Mario Martelli Maria Patrizia Pera 《Journal of Fixed Point Theory and Applications》2007,2(2):293-312
We obtain a necessary as well as a sufficient condition for the existence of bifurcation points of a coincidence equation,
and, in particular, of a parametrized fixed point problem. In both cases the trivial solutions are assumed to form a finite-dimensional
submanifold of a Banach manifold. An application is given to a delay differential equation on a manifold: we detect periodic
solutions that rotate close to an equilibrium point.
To Albrecht Dold and Edward Fadell, superb mathematicians and first rate friends 相似文献
9.
Since the early seventies flows with the Lefschetz property were studied by several authors. In this paper a Lefschetz formula
is proved for the geodesic flow of a compact locally symmetric space. The flow is described in terms of actions of split tori
of various dimensions and the geometric side of the Lefschetz formula is a sum over closed geodesics which correspond to a
given torus. The cohomological side is given in terms of Lie algebra cohomology. 相似文献
10.
11.
Wei ChenBingwen Liu 《Journal of Computational and Applied Mathematics》2011,235(8):2090-2097
In this paper, we study the existence and exponential convergence of positive almost periodic solutions for the generalized Nicholson’s blowflies model with multiple time-varying delays. Under proper conditions, we establish some criteria to ensure that the solutions of this model converge locally exponentially to a positive almost periodic solution. Moreover, we give some examples to illustrate our main results. 相似文献
12.
In this paper, we first introduce the concepts and properties of the square-mean weighted pseudo almost automorphy and the square-mean bi-almost automorphy for a stochastic process. With these preliminary settings and by virtue of the theory of the semigroups of the operators, the Banach fixed point theorem and the stochastic analysis techniques, we investigate the well-posedness of the square-mean weighted pseudo almost automorphic solutions for a general class of non-autonomous stochastic evolution equations that satisfy either global or only local Lipschitz condition. Moreover, we estimate the boundedness of attractive domain for the case where the only local Lipschitz condition is taken into account. Finally, we provide two illustrative examples to show the practical usefulness of the analytical results that we establish in the paper. 相似文献
13.
Existence and Stability of Periodic Solutions of a Duffing Equation by Using a New Maximum Principle
The purpose of this paper is to obtain new criteria for existence and asymptotic stability of periodic solutions of a Duffing equation x + cx + g(t, x) = 0, taking advantage of a new maximum principle with Lp-conditions combined with known relations between upper and lower solutions, topological degree and stability.Partially supported by D.G.I. BFM2002-01308, Ministerio Ciencia y Tecnología, Spain. 相似文献
14.
We consider the existence of solutions of a nonlinear Riemann-Hilbert problem for a quasilinear -equation on a bordered Riemann surface.
The first author was supported in part by a grant ``Analiza in geometrija' P1-0291 from the Ministry of Higher Education,
Science and Technology of the Republic of Slovenia.
The second author was supported in part by grants from FEDER y Ministerio de Ciencia y Tecnología numbers BFM2001-3894 MTM
2004-05878 and Consejería de Educacion Cultura y Deportes del Gobierno de Canarias, PI 2001/091. 相似文献
15.
Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the corresponding non-homogeneous Ricci-flat metrics with holonomy contained
in G2. In the process we also find a new metric with exceptional holonomy.
Received: 20 September 相似文献
16.
17.
Zalman Rubinstein 《Aequationes Mathematicae》1981,23(1):108-117
Several characteristic functional equations satisfied by classes of polynomials of bounded degree are examined in connection with certain generalizations of the Morera-Carleman Theorem. Certain functional equations which have nonanalytic polynomial solutions are also considered. 相似文献
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19.
Jinkui Wan 《Journal of Pure and Applied Algebra》2011,215(7):1569-1581
We formulate a theory of invariants for the spin symmetric group in some suitable modules which involve the polynomial and exterior algebras. We solve the corresponding graded multiplicity problem in terms of specializations of the Schur Q-functions and a shifted q-hook formula. In addition, we provide a bijective proof for a formula of the principal specialization of the Schur Q-functions. 相似文献
20.
Sándor Szabó 《Aequationes Mathematicae》1989,38(2-3):186-191
Summary If a finite abelian (p, q)-group whosep-Sylow subgroup is cyclic is factorized by subsets of cardinalitiesq or a power ofp, then at least one of the factors is periodic. 相似文献