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1.
Let X be a metric space andμa finite Borel measure on X. Let pμq,t and pμq,t be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x,r))q(2r)t, where q, t∈R. For any compact set E of finite packing premeasure the authors prove: (1) if q≤0 then pμq,t(E)=pμq,t(E);(2)if q>0 andμis doubling on E then pμq,t(E) and pμq,t(E) are both zero or neither. 相似文献
2.
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
3.
Let be a time scale such that . By the Schauder fixed-point theorem and the upper and lower solution method, we present some existence criteria of the positive solution of m-point singular p-Laplacian dynamic equation with boundary conditions , where φp(s)=|s|p-2s with p>1, is continuous for i=1,2,…,m-1 and nonincreasing if . The nonlinear term may be singular in its dependent variable and is allowed to change sign. Our results are new even for the corresponding differential and difference equations . As an application, an example is given to illustrate our result. 相似文献
4.
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
5.
We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for an≡1, bn=−Cn−β (), one has on (−2,2), and near x=2, where 相似文献
6.
Le Thi Phuong Ngoc Le Khanh Luan Tran Minh Thuyet Nguyen Thanh Long 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5799-5819
In this paper, we consider the following nonlinear wave equation (1) where , , μ, f, g are given functions. To problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In the case of , , μ(z)≥μ0>0, μ1(z)≥0, for all , and , , , a weak solution uε1,ε2(x,t) having an asymptotic expansion of order N+1 in two small parameters ε1, ε2 is established for the following equation associated to (1)2,3: (2) 相似文献
7.
Let be an orthonormal Jacobi polynomial of degree k. We will establish the following inequality:where δ-1<δ1 are appropriate approximations to the extreme zeros of . As a corollary we confirm, even in a stronger form, T. Erdélyi, A.P. Magnus and P. Nevai conjecture [T. Erdélyi, A.P. Magnus, P. Nevai, Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994) 602–614] by proving thatin the region . 相似文献
8.
Let , and for k=0,1,…, denote the orthonormalized Jacobi polynomial of degree k. We discuss the construction of a matrix H so that there exist positive constants c, c1, depending only on H, α, and β such that Specializing to the case of Chebyshev polynomials, , we apply this theory to obtain a construction of an exponentially localized polynomial basis for the corresponding L2 space. 相似文献
9.
We prove the Marcinkiewicz–Zygmund Strong Law of Large Numbers for U-statistics of strictly stationary, absolutely regular observations (ξi)i≥1. Under suitable moment conditions and conditions on the mixing rate, we show that for some γ≥0, in the non-degenerate case, and in the degenerate case. 相似文献
10.
We introduce the family of linear operatorsassociated to a certain “admissible bunch” of operators St, t>0, acting on , and investigate the approximation properties of this family as α→0+. We give some applications to the Riesz and the Bessel potentials generated by the ordinary (Euclidean) and generalized translations. 相似文献