共查询到20条相似文献,搜索用时 874 毫秒
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.
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
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.
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
5.
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
6.
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
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
11.
Ivan Kiguradze Tariel Kiguradze 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):1914-1933
In the rectangle Ω=[0,a]×[0,b] for the nonlinear hyperbolic equation the boundary value problems of the type are considered, where and are linear bounded functionals.Sufficient conditions of solvability and unique solvability of the general problem and its particular cases (Nicoletti type, Dirichlet, Lidstone and Periodic problems) are established. 相似文献
12.
Global stability of a difference equation with maximum 总被引:1,自引:1,他引:0
Stevo Stevi 《Applied mathematics and computation》2009,210(2):525-529
We prove that every positive solution to the difference equationwhere , i=1,…,k, converges to the following quantity , confirming a quite recent conjecture of interest. We also prove another result on global convergence which concerns some cases when not all αi,i=1,…,k belong to the interval (0, 1). 相似文献
13.
Let p be a trigonometric polynomial, non-negative on the unit circle . We say that a measure σ on belongs to the polynomial Szegő class, if , σs is singular, andFor the associated orthogonal polynomials {n}, we obtain pointwise asymptotics inside the unit disc . Then we show that these asymptotics hold in L2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators. 相似文献
14.
Integral inequalities for the Hilbert transform applied to a nonlocal transport equation 总被引:2,自引:0,他引:2
Antonio Crdoba Diego Crdoba Marco A. Fontelos 《Journal de Mathématiques Pures et Appliquées》2006,86(6):529-540
We prove several weighted inequalities involving the Hilbert transform of a function f(x) and its derivative. One of those inequalities, is used to show finite time blow-up for a transport equation with nonlocal velocity. 相似文献
15.
A family of orthonormal polynomials on the unit ball Bd of with respect to the inner productwhere Δ is the Laplace operator, is constructed explicitly. 相似文献
16.
Let have a multiple zero α with integer multiplicity m≥1 and be analytic in a sufficiently small neighborhood of α. For parameter-controlled Newton-secant method defined by we investigate the maximal order of convergence and the theoretical asymptotic error constant by seeking the relationship between parameters λ and μ. For various test functions, the numerical method has shown a satisfactory result with high-precision Mathematica programming. 相似文献
17.
Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source 总被引:1,自引:0,他引:1
In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions gi(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property. 相似文献
18.
Let be a bounded domain such that 0Ω. Denote by , the set of all complex polynomials of degree at most n. Let where . We relate the maximal polynomial range to the geometry of Ω. 相似文献
19.
In this paper, we consider a Dirichlet problem involving the p(x)-Laplacian of the type We prove the existence of infinitely many non-negative solutions of the problem by applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces. 相似文献
20.
Thierry Cazenave Flvio Dickstein Fred B. Weissler 《Journal of Mathematical Analysis and Applications》2009,360(2):537-547
In this paper, we consider the nonlinear heat equation(NLH)
ut−Δu=|u|αu,