共查询到20条相似文献,搜索用时 52 毫秒
1.
Let be a nontrivial involution, i.e., R=R−1≠±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
In this paper the homogenization of degenerate nonlinear parabolic equations where a(t,y,λ) is periodic in (t,y), is studied via a weighted compensated compactness result. 相似文献
9.
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
10.
Construction of highly stable parallel two-step Runge–Kutta methods for delay differential equations
Z. Bartoszewski Z. Jackiewicz 《Journal of Computational and Applied Mathematics》2008,220(1-2):257-270
It is shown that any A-stable two-step Runge–Kutta method of order and stage order for ordinary differential equations can be extended to the P-stable method of uniform order for delay differential equations. 相似文献
11.
G.R. Cirmi S. Leonardi J. Star 《Nonlinear Analysis: Theory, Methods & Applications》2008,68(12):3609-3624
We prove that if a vector-function f belongs to the Morrey space , with , n≥3, N≥2, λ]0,n−2], and u is the solution of the system then Du belongs to the space , for any , provided the matrix of bounded measurable coefficients (Aij) has sufficiently small dispersion of the eigenvalues. 相似文献
12.
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
13.
Let be a bounded Lipschitz domain, a suitably quasiconvex integrand and consider the energy functional over the space of measure preserving maps In this paper we discuss the question of existence of multiple strong local minimizers for over . Moreover, motivated by their significance in topology and the study of mapping class groups, we consider a class of maps, referred to as twists, and examine them in connection with the corresponding Euler–Lagrange equations and investigate various qualitative properties of the resulting solutions, the stationary twists. Particular attention is paid to the special case of the so-called p-Dirichlet energy, i.e., when . 相似文献
14.
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
15.
By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with state dependent delays where (i,j=1,2,…,n) are ω-periodic functions and (i=1,2,…,n) are ω-periodic functions with respect to their first arguments, respectively. 相似文献
16.
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
17.
Given an integrable function f, we are concerned with the construction of a spline Hn(f) of degree n with prescribed knots that satisfies the histopolation conditionsfor some fixed . Additionally, the resulting spline operator should be local and reproduce all polynomials of degree n. Our approach of generating such a histospline is based on a local spline interpolation operator that is exact for all polynomials of degree n. 相似文献
18.
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
19.
In this paper, we will consider the following multipoint boundary value problem for the following second-order dynamic equations on time scales where :RR is an increasing homeomorphism and positive homomorphism and (0)=0. By using fixed point theorems, we obtain an existence theorem of positive solutions for the above boundary value problem, which includes and improve some related results in the relevant literature. As an application, an example to demonstrate our results is given. 相似文献
20.
The goal of the paper is to prove generalizations of the classical Plancherel–Polya inequalities in which point-wise sampling of functions (δ-distributions) is replaced by more general compactly supported distributions on . As an application it is shown that a function , 1p∞, which is an entire function of exponential type is uniquely determined by a set of numbers {Ψj(f)}, , where {Ψj}, , is a countable sequence of compactly supported distributions. In the case p=2 a reconstruction method of a Paley–Wiener function f from a sequence of samples {Ψj(f)}, , is given. This method is a generalization of the classical result of Duffin–Schaeffer about exponential frames on intervals. 相似文献