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1.
In this paper, we afford some sufficient conditions to guarantee the existence of multiple positive solutions for the nonlinear m-point boundary-value problem for the one-dimensional p-Laplacian 相似文献
(φp(u′))′+f(t,u)=0, t(0,1),
2.
With the notation
,we prove the following result.Theorem 1. Assume that p is a trigonometric polynomial of degree at most n with real coefficients that satisfiesThenwithWe also prove thatandfor every
, where
denotes the collection of all trigonometric polynomials of the form 相似文献
||p||L2(K)An1/2 and ||p′||L2(K)Bn3/2.
M4(p)−M2(p)M2(p)
M2(p)−M1(p)10−31M2(p)
3.
Miroslav Bartu
ek 《Journal of Mathematical Analysis and Applications》2003,280(2):232-240
In the paper sufficient conditions are given under which the differential equation y(n)=f(t,y,…,y(n−2))g(y(n−1)) has a singular solution y :[T,τ)→R, τ<∞ fulfilling 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.
We study generalized equations of the following form: (render) where f is Fréchet differentiable in a neighborhood of a solution x* of (*) and g is Fréchet differentiable at x* and where F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying which is super-linearly convergent to a solution of (*). We also present other versions of this iterative procedure that have superlinear and quadratic convergence, respectively. 相似文献
0f(x)+g(x)+F(x),
6.
Thomas Kühn Hans-Gerd Leopold Winfried Sickel Leszek Skrzypczak 《Journal of Approximation Theory》2003,121(2):244-268
Let
be the radial subspace of the Besov space
. We prove the independence of the asymptotic behavior of the entropy numbersfrom the difference s0−s1 as long as the embedding itself
is compact. In fact, we shall show thatThis is in a certain contrast to earlier results on entropy numbers in the context of Besov spaces Bp,qs(Ω) on bounded domains Ω. 相似文献
7.
N. Ghoussoub X. S. Kang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2004,21(6):3934-793
Unlike the non-singular case s=0, or the case when 0 belongs to the interior of a domain Ω in
(n3), we show that the value and the attainability of the best Hardy–Sobolev constant on a smooth domain Ω, when 0<s<2,
, and when 0 is on the boundary ∂Ω are closely related to the properties of the curvature of ∂Ω at 0. These conditions on the curvature are also relevant to the study of elliptic partial differential equations with singular potentials of the form: where f is a lower order perturbative term at infinity and f(x,0)=0. We show that the positivity of the sectional curvature at 0 is relevant when dealing with Dirichlet boundary conditions, while the Neumann problems seem to require the positivity of the mean curvature at 0. 相似文献
8.
Gradimir V. Milovanovi Miodrag M. Spalevi 《Journal of Computational and Applied Mathematics》2002,140(1-2)
Let dλ(t) be a given nonnegative measure on the real line
, with compact or infinite support, for which all moments
exist and are finite, and μ0>0. Quadrature formulas of Chakalov–Popoviciu type with multiple nodeswhere σ=σn=(s1,s2,…,sn) is a given sequence of nonnegative integers, are considered. A such quadrature formula has maximum degree of exactness dmax=2∑ν=1nsν+2n−1 if and only ifThe proof of the uniqueness of the extremal nodes τ1,τ2,…,τn was given first by Ghizzetti and Ossicini (Rend. Mat. 6(8) (1975) 1–15). Here, an alternative simple proof of the existence and the uniqueness of such quadrature formulas is presented. In a study of the error term R(f), an influence function is introduced, its relevant properties are investigated, and in certain classes of functions the error estimate is given. A numerically stable iterative procedure, with quadratic convergence, for determining the nodes τν, ν=1,2,…,n, which are the zeros of the corresponding σ-orthogonal polynomial, is presented. Finally, in order to show a numerical efficiency of the proposed procedure, a few numerical examples are included. 相似文献
9.
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
10.
Consider the permanence and global asymptotic stability of models governed by the following Lotka-Volterra-type system: , with initial conditions . We define x0(t) = xn+1(t)≡0 and suppose that φi(t), 1 ≤ i ≤ n, are bounded continuous functions on [t0, + ∞) and γi, αi, ci > 0,γi,j ≥ 0, for all relevant i,j.Extending a technique of Saito, Hara and Ma[1] for n = 2 to the above system for n ≥ 2, we offer sufficient conditions for permanence and global asymptotic stability of the solutions which improve the well-known result of Gopalsamy. 相似文献
xi(t) = φi(t) ≥ o, t ≤ t0, and φi(t0) > 0. 1 ≤ i ≤n
11.
J. Lang 《Journal of Approximation Theory》2006,140(2):141-146
Consider the Hardy-type operator T : Lp(a,b)→Lp(a,b),-∞a<b∞, which is defined byIt is shown thatwhere ρn(T) stands for any of the following: the Kolmogorov n-width, the Gel’fand n-width, the Bernstein n-width or the nth approximation number of T. 相似文献
12.
Let p(n) denote the number of unrestricted partitions of n. For i=0, 2, let pi(n) denote the number of partitions π of n such that . Here denotes the number of odd parts of the partition π and π′ is the conjugate of π. Stanley [Amer. Math. Monthly 109 (2002) 760; Adv. Appl. Math., to appear] derived an infinite product representation for the generating function of p0(n)-p2(n). Recently, Swisher [The Andrews–Stanley partition function and p(n), preprint, submitted for publication] employed the circle method to show that(i) and that for sufficiently large n (ii) In this paper we study the even/odd dissection of the Stanley product, and show how to use it to prove (i) and (ii) with no restriction on n. Moreover, we establish the following new result:Two proofs of this surprising inequality are given. The first one uses the Göllnitz–Gordon partition theorem. The second one is an immediate corollary of a new partition inequality, which we prove in a combinatorial manner. Our methods are elementary. We use only Jacobi's triple product identity and some naive upper bound estimates. 相似文献
13.
In this article, the authors consider equation ut = div(ψ(Гu)A(|Du|2)Du) -(u- I), where ψ is strictly positive and Г is a known vector-valued mapping, A: R → R is decreasing and A(s) ~ 1/√a as s → ∞. This kind of equation arises naturally from image denoising. For an initial datum I ∈ BVloc ∩ L∞, the existence of BV solutions to the initial value problem of the equation is obtained. 相似文献
14.
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
15.
16.
Let ζ be the Riemann zeta function and δ(x)=1/(2x-1). For all x>0 we have
(1-δ(x))ζ(x)+αδ(x)<ζ(x+1)<(1-δ(x))ζ(x)+βδ(x),