首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 220 毫秒
1.
We prove the existence of nontrivial critical points for a class of superquadratic nonautonomous second-order Hamiltonian systems by applying condition (C) to critical point theory, and some new solvability conditions of nontrivial periodic solutions are obtained.  相似文献   

2.
The present paper is concerned with asymptotic behaviours of the solutions to the micropolar fluid motion equations in R2. Upper and lower bounds are derived for the L2 decay rates of higher order derivatives of solutions to the micropolar fluid flows. The findings are mainly based on the basic estimates of the linearized micropolar fluid motion equations and generalized Gronwall type argument.  相似文献   

3.
We obtain a strong solution in charge critical space L2(R) of the Thirring system and Federbusch equations in one space dimension by using solution representation of the models. The uniqueness is obtained for the solution ΨL([0,T];L2(R)∩L4(R)). A decay of local charge and asymptotic behavior of the field can be shown directly.  相似文献   

4.
Invariant foliations over inertial manifolds of partial differential equations under numerical discretizations are studied. It is proved that the numerical method considered as a discrete dynamical system has C1-close invariant foliations. The rate of the C1-convergence is estimated as well.  相似文献   

5.
R-Boundedness is a randomized boundedness condition for sets of operators which in recent years has found many applications in the maximal regularity theory of evolution equations, stochastic evolution equations, spectral theory and vector-valued harmonic analysis. However, in some situations additional geometric properties such as Pisier's property (α) are required to guaranty the R-boundedness of a relevant set of operators. In this paper we show that a weaker property called semi-R-boundedness can be used to avoid these geometric assumptions in the context of Schauder decompositions and the H-calculus. Furthermore, we give weaker conditions for stochastic integrability of certain convolutions.  相似文献   

6.
By a ball-covering B of a Banach space X, we mean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere SX of X; and X is said to have the ball-covering property (BCP) provided it admits a ball-covering by countably many balls. In this note we give a natural example showing that the ball-covering property of a Banach space is not inherited by its subspaces; and we present a sharp quantitative version of the recent Fonf and Zanco renorming result saying that if the dual X of X is w separable, then for every ε>0 there exist a (1+ε)-equivalent norm on X, and an R>0 such that in this new norm SX admits a ball-covering by countably many balls of radius R. Namely, we show that R=R(ε) can be taken arbitrarily close to (1+ε)/ε, and that for X=?1[0,1] the corresponding R cannot be equal to 1/ε. This gives the sharp order of magnitude for R(ε) as ε→0.  相似文献   

7.
We investigate a limiting uniqueness criterion to the Navier-Stokes equations. We prove that the mild solution is unique under the class , where bmo-1 is the “critical” space including Ln. As an application of uniqueness theorem, we also consider the local well-posedness of Navier-Stokes equations in bmo-1.  相似文献   

8.
In this paper, the solution of the nonlinear evolution inclusion problem of the form u(t)+B(t,u(t))∋f(t) is studied. In this problem, the operators are of type (M) or type (S+), which are different from those of pseudo-monotone operators that had been studied by many authors. At the same time, we study the perturbation problem. In fact, many kinds of evolution equations can be generalized by this problem. The former results are improved and generalized by our conclusions, and we will give more applications.  相似文献   

9.
We study the long time behavior of solutions for damped wave equations with absorption. These equations are generally accepted as models of wave propagation in heterogeneous media with space-time dependent friction a(t,x)ut and nonlinear absorption |u|p−1u (Ikawa (2000) [17]). We consider 1<p<(n+2)/(n−2) and separable a(t,x)=λ(x)η(t) with λ(x)∼(1+|x|)α and η(t)∼(1+t)β satisfying conditions (A1) or (A2) which are given. The main results are precise decay estimates for the energy, L2 and Lp+1 norms of solutions. We also observe the following behavior: if α∈[0,1), β∈(−1,1) and 0<α+β<1, there are three different regions for the decay of solutions depending on p; if α∈(−,0) and β∈(−1,1), there are only two different regions for the decay of the solutions depending on p.  相似文献   

10.
Let A be the C-algebra associated to an arbitrary continuous field of C-algebras. We give a necessary and sufficient condition for A to have the ideal property and, if moreover A is separable, we give a necessary and sufficient condition for A to have the projection property. Some applications of these results are given. We also prove that “many” crossed products of commutative C-algebras by discrete, amenable groups have the projection property, generalizing some of our previous results.  相似文献   

11.
Schonbek [M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. Partial Differential Equations 7 (1982) 959-1000] obtained the strong convergence of uniform bounded approximate solutions to hyperbolic scalar equation under the assumption that the flux function is strictly convex. While in this paper, by constructing four families of Lax entropies, we succeed in dealing with the non-convexity with the aid of the well-known Bernstein-Weierstrass theorem, and obtaining the strong convergence of uniform L or bounded viscosity solutions for scalar conservation law without convexity.  相似文献   

12.
Short proofs of the following results concerning a bounded conformal map g of the unit disc D are presented: (1) logg belongs to the Dirichlet space if and only if the Schwarzian derivative Sg of g satisfies Sg(z)(1−2|z|)∈L2(D); (2) loggVMOA if and only if 2|Sg(z)|3(1−2|z|) is a vanishing Carleson measure on D. Analogous results for Besov and Qp,0 spaces are also given.  相似文献   

13.
In this paper we shall study Hardy spaces of analytic functions in a strip S. Our main result is on one hand an intrinsic characterization of the spaces and on the second that polynomials are dense. We also present an orthogonal (in H2(S)) basis of polynomials.  相似文献   

14.
In this paper we present some regularity results for solutions to the system −Δu=σ(u)2|∇φ|, div(σ(u)∇φ)=0 in the case where σ(u) is allowed to oscillate between 0 and a positive number as u→∞. In particular, we show that u is locally bounded if σ(u) is bounded below by a suitable exponential function.  相似文献   

15.
The stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors, but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay. The main aim of this paper is to close this gap. We establish criteria of pth moment ψγ(t)-bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay, and we also illustrate the result with an example.  相似文献   

16.
In this paper, we will study the isometric extension problem for L1-spaces and prove that every surjective isometry from the unit sphere of L1(μ) onto that of a Banach space E can be extended to a linear surjective isometry from L1(μ) onto E. Moreover, we introduce the approximate isometric extension problem and show that, if E and F are Banach spaces and E satisfies the property (m) (special cases are L(Γ), C0(Ω) and L(μ)), then every bijective ?-isometry between the unit spheres of E and F can be extended to a bijective 5?-isometry between their closed unit balls. At last, we will give an example to show that the surjectivity assumption cannot be omitted. Using this, we solve the non-surjective isometric extension problem in the negative.  相似文献   

17.
For a measurable space (Ω,A), let ?(A) be the closure of span{χA:AA} in ?(Ω). In this paper we show that a sufficient and necessary condition for a real-valued finitely additive measure μ on (Ω,A) to be countably additive is that the corresponding functional ?μ defined by (for x?(A)) is w*-sequentially continuous. With help of the Yosida-Hewitt decomposition theorem of finitely additive measures, we show consequently that every continuous functional on ?(A) can be uniquely decomposed into the ?1-sum of a w*-continuous functional, a purely w*-sequentially continuous functional and a purely (strongly) continuous functional. Moreover, several applications of the results to measure extension are given.  相似文献   

18.
Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation p|cosp(φ)|+p|sinp(φ)|=1. The p-generalized radius coordinate of a point ξRn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.  相似文献   

19.
We make some comparisons concerning the induced infinitesimal Kobayashi metric, the induced Siegel metric, the L2 Bergman metric, the Teichmüller metric and the Weil-Petersson metric on the Teichmüller space of a compact Riemann surface of genus g?2. As a consequence, among others, we show that the moduli space has finite volume with respect to the L2 Bergman metric. This answers a question raised by Nag in 1989.  相似文献   

20.
The subject of this paper is an analytic approximate method for stochastic functional differential equations whose coefficients are functionals, sufficiently smooth in the sense of Fréchet derivatives. The approximate equations are defined on equidistant partitions of the time interval, and their coefficients are general Taylor expansions of the coefficients of the initial equation. It will be shown that the approximate solutions converge in the Lp-norm and with probability one to the solution of the initial equation, and also that the rate of convergence increases when degrees in Taylor expansions increase, analogously to real analysis.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号