共查询到20条相似文献,搜索用时 46 毫秒
1.
The aim of this paper is to establish the local convergence of the steepest descent method for C1-functionals defined on an infinite-dimensional Hilbert space H, under a Palais–Smale-type condition. The functionals f under consideration are also assumed to have a locally Lipschitz continuous gradient operator f. Our approach is based on the solutions of the ordinary differential equation . 相似文献
2.
Nguyen Thanh Chung Hoang Quoc Toan 《Journal of Mathematical Analysis and Applications》2009,360(2):422-431
This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , hi (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (Fu,Fv)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199]. 相似文献
3.
Let M be a connected binary matroid having no -minor. Let be a collection of cocircuits of M. We prove there is a circuit intersecting all cocircuits of if either one of two things hold:
- (i) For any two disjoint cocircuits and in it holds that .
- (ii) For any two disjoint cocircuits and in it holds that .
4.
Let H, V be two real Hilbert spaces such that VH with continuous and dense imbedding, and let FC1(V) be convex. By using differential inequalities, a close-to-optimal ultimate bound of the energy is obtained for solutions in to u″+cu′+bu+F(u)=f(t) whenever . 相似文献
5.
We consider an aggregation equation in , d2, with fractional dissipation: ut+(uK*u)=−νΛγu, where ν0, 0<γ<1, and K(x)=e−|x|. We prove a refined blowup criteria by which the global existence of solutions is controlled by its norm, for any . We prove the finite time blowup of solutions for a general class of nonsymmetric initial data. The argument presented works for both the inviscid case ν=0 and the supercritical case ν>0 and 0<γ<1. Additionally, we present new proofs of blowup which does not use free energy arguments. 相似文献
6.
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
7.
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
8.
We consider linearly ordered, Archimedean dimension groups (G,G+,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G+,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C*-algebra is the Fibonacci C*-algebra. 相似文献
9.
We analyze the asymptotic behavior of solutions to nonlinear elliptic equation Δu±|u|q=b(x)f(u) in Ω, subject to the singular boundary condition u(x)=∞ as , where Ω is a smooth bounded domain in RN, for some , and . Our approach employs Karamata regular variation theory combined with the method of lower and supper solution. 相似文献
10.
Let be an ideal of subsets of a metric space X,d. This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of which reduces to ordinary continuity when consists of the finite subsets of X and agrees with uniform continuity on members of when is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions. 相似文献
11.
The paper deals with random vectors in , possessing the stochastic representation , where R is a positive random radius independent of the random vector and is a non-singular matrix. If is uniformly distributed on the unit sphere of , then for any integer m<d we have the stochastic representations and , with W≥0, such that W2 is a beta distributed random variable with parameters m/2,(d−m)/2 and (U1,…,Um),(Um+1,…,Ud) are independent uniformly distributed on the unit spheres of and , respectively. Assuming a more general stochastic representation for in this paper we introduce the class of beta-independent random vectors. For this new class we derive several conditional limiting results assuming that R has a distribution function in the max-domain of attraction of a univariate extreme value distribution function. We provide two applications concerning the Kotz approximation of the conditional distributions and the tail asymptotic behaviour of beta-independent bivariate random vectors. 相似文献
12.
A series is called a pointwise universal trigonometric series if for any , there exists a strictly increasing sequence of positive integers such that converges to f(z) pointwise on . We find growth conditions on coefficients allowing and forbidding the existence of a pointwise universal trigonometric series. For instance, if as |n|→∞ for some ε>0, then the series Sa cannot be pointwise universal. On the other hand, there exists a pointwise universal trigonometric series Sa with as |n|→∞. 相似文献
13.
For the reflected diffusion generated by on a connected and complete Riemannian manifold M with empty or convex boundary, we establish some sharp estimates of supxM|G|(x) of the Poisson equation in terms of the dimension, the diameter and the lower bound of curvature. Applications to transportation-information inequality, to Cheeger's isoperimetric inequality and to Gaussian concentration inequality are given. Several examples are provided. 相似文献
14.
On new Bloch-type spaces 总被引:2,自引:0,他引:2
Stevo Stevi 《Applied mathematics and computation》2009,215(2):841-849
We introduce a new Bloch-type space, so called, the logarithmic Bloch-type space on the unit disc , as the space of all holomorphic functions f on such thatwhere α>0 and β0, and present some basic properties of the space. A necessary and a sufficient condition for a function with Hadamard gaps to belong to the logarithmic Bloch-type space are given, as well as some applications of these results to a composition operator. 相似文献
15.
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,