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1.
We study the large time asymptotic behavior, in Lp (1p∞), of higher derivatives Dγu(t) of solutions of the nonlinear equation(1) where the integers n and θ are bigger than or equal to 1, a is a constant vector in with . The function ψ is a nonlinearity such that and ψ(0)=0, and is a higher order elliptic operator with nonsmooth bounded measurable coefficients on . We also establish faster decay when . 相似文献
2.
We consider in this paper the problem(0.1) where Ω is the unit ball in centered at the origin, 0α<pN, β>0, N8, p>1, qε>1. Suppose qε→q>1 as ε→0+ and qε,q satisfy respectively we investigate the asymptotic behavior of the ground state solutions (uε,vε) of (0.1) as ε→0+. We show that the ground state solutions concentrate at a point, which is located at the boundary. In addition, the ground state solution is non-radial provided that ε>0 is small. 相似文献
3.
The nth cyclic function is defined by
We prove that if k is an integer with 1kn−1, then
holds for all positive real numbers x with the best possible constantsα=1 and β= 2n-k over n. 相似文献
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4.
We study diagonal multipoint Padé approximants to functions of the form where R is a rational function and λ is a complex measure with compact regular support included in , whose argument has bounded variation on the support. Assuming that interpolation sets are such that their normalized counting measures converge sufficiently fast in the weak-star sense to some conjugate-symmetric distribution σ, we show that the counting measures of poles of the approximants converge to , the balayage of σ onto the support of λ, in the weak* sense, that the approximants themselves converge in capacity to F outside the support of λ, and that the poles of R attract at least as many poles of the approximants as their multiplicity and not much more. 相似文献
5.
Let M be a CR manifold. The main results of this paper are the following:
- When M is real analytic, a semi-global Hartogs extension phenomenon occurs for real analytic CR functions if and only if M is nowhere strictly pseudoconvex and
.
- When M is a standard manifold, the Hartogs–Bochner extension phenomenon occurs for non-CR-confined domains if and only if M is nowhere strictly pseudoconvex and dimCRM2.
- If M is a smooth submanifold of
foliated by complex curves, a semi-global Hartogs–Bochner extension phenomenon occurs for smooth non-CR-confined domains if and only if dimCRM2.
- If M is a real analytic nowhere strictly pseudoconvex manifold and if Ω is a sufficiently small domain in M, a hyperfunction which is real analytic in a neighborhood of bΩ and CR in a neighborhood of
is in fact real analytic on Ω.
Mots-clé: Hartogs; Variétés CR; Nulle part strictement pseudoconvexe; Hyperfonction; Représentation intégraleMots-clé: Hartogs; CR manifold; Nowhere strictly pseudoconvex; Hyperfunction; Integral representation 相似文献
6.
In this paper, we study the existence of periodic solutions of the second order differential equations x″+f(x)x′+g(x)=e(t). Using continuation lemma, we obtain the existence of periodic solutions provided that F(x) () is sublinear when x tends to positive infinity and g(x) satisfies a new condition where M, d are two positive constants. 相似文献
7.
In this paper, some properties of Ramsey numbers are studied, and the following results are presented.
- 1. (1) For any positive integers k1, k2, …, km l1, l2, …, lm (m> 1), we have .
- 2. (2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have . Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties.
8.
We consider the following nonlinear elliptic equation with singular nonlinearity: where α>β>1, a>0, and Ω is an open subset of , n2. Let uH1(Ω) with and be a nonnegative stationary solution. If we denote the zero set of u by we shall prove that the Hausdorff dimension of Σ is less than or equal to . 相似文献
9.
A. Bultheel P. González-Vera E. Hendriksen O. Njåstad 《Journal of Approximation Theory》1997,89(3):344-371
In Akhiezer's book [“The Classical Moment Problem and Some Related Questions in Analysis,” Oliver & Boyd, Edinburghasol;London, 1965] the uniqueness of the solution of the Hamburger moment problem, if a solution exists, is related to a theory of nested disks in the complex plane. The purpose of the present paper is to develop a similar nested disk theory for a moment problem that arises in the study of certain orthogonal rational functions. Let {αn}∞n=0be a sequence in the open unit disk in the complex plane, let
(
/|αk|=−1 whenαk=0), and let
We consider the following “moment” problem: Given a positive-definite Hermitian inner product ·, · on
×
, find a non-decreasing functionμon [−π, π] (or a positive Borel measureμon [−π,π)) such that
In particular we give necessary and sufficient conditions for the uniqueness of the solution in the case that
If this series diverges the solution is always unique. 相似文献
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10.
Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws 总被引:1,自引:0,他引:1
We consider a system of heat equations ut=Δu and vt=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p,q>0, 0≤α<1 and 0≤β<p. 相似文献
11.
Let F be any field. Let p(F) be the characteristic of F if F is not of characteristic zero, and let p(F)=+∞ otherwise. Let A1,…,An be finite nonempty subsets of F, and let with k{1,2,3,…}, a1,…,anF{0} and degg<k. We show that When kn and |Ai|i for i=1,…,n, we also have consequently, if nk then for any finite subset A of F we have In the case n>k, we propose a further conjecture which extends the Erdős–Heilbronn conjecture in a new direction. 相似文献
12.
Salim A. Messaoudi Belkacem Said-Houari 《Journal of Mathematical Analysis and Applications》2009,360(2):459-475
Fernández Sare and Rivera [H.D. Fernández Sare, J.E. Muñoz Rivera, Stability of Timoshenko systems with past history, J. Math. Anal. Appl. 339 (1) (2008) 482–502] considered the following Timoshenko-type system
ρ1φtt−K(φx+ψ)x=0,