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 46 毫秒
1.
We study the isochronicity of centers at OR2 for systems , , where A,BR[x,y], which can be reduced to the Liénard type equation. Using the so-called C-algorithm we have found 27 new multiparameter isochronous centers.  相似文献   

2.
We determine the principal eigenvalues of the linear indefinite weight problem Moreover, we investigate the existence of positive solutions for the corresponding nonlinear indefinite weight problem, where g:[0,1]→R is a continuous function which attains both positive and negative values, fC(R,R), and r is a parameter.  相似文献   

3.
In this paper we classify the centers localized at the origin of coordinates, and their isochronicity for the polynomial differential systems in R2 of degree d that in complex notation z=x+iy can be written as where j is either 0 or 1. If j=0 then d?5 is an odd integer and n is an even integer satisfying 2?n?(d+1)/2. If j=1 then d?3 is an integer and n is an integer with converse parity with d and satisfying 0<n?[(d+1)/3] where [⋅] denotes the integer part function. Furthermore λR and A,B,C,DC. Note that if d=3 and j=0, we are obtaining the generalization of the polynomial differential systems with cubic homogeneous nonlinearities studied in K.E. Malkin (1964) [17], N.I. Vulpe and K.S. Sibirskii (1988) [25], J. Llibre and C. Valls (2009) [15], and if d=2, j=1 and C=0, we are also obtaining as a particular case the quadratic polynomial differential systems studied in N.N. Bautin (1952) [2], H. Zoladek (1994) [26]. So the class of polynomial differential systems here studied is very general having arbitrary degree and containing the two more relevant subclasses in the history of the center problem for polynomial differential equations.  相似文献   

4.
We compute the Fredholm index, index(DA), of the operator DA=(d/dt)+A on L2(R;H) associated with the operator path , where (Af)(t)=A(t)f(t) for a.e. tR, and appropriate fL2(R;H), via the spectral shift function ξ(⋅;A+,A) associated with the pair (A+,A) of asymptotic operators A±=A(±∞) on the separable complex Hilbert space H in the case when A(t) is generally an unbounded (relatively trace class) perturbation of the unbounded self-adjoint operator A.We derive a formula (an extension of a formula due to Pushnitski) relating the spectral shift function ξ(⋅;A+,A) for the pair (A+,A), and the corresponding spectral shift function ξ(⋅;H2,H1) for the pair of operators in this relative trace class context,This formula is then used to identify the Fredholm index of DA with ξ(0;A+,A). In addition, we prove that index(DA) coincides with the spectral flow of the family {A(t)}tR and also relate it to the (Fredholm) perturbation determinant for the pair (A+,A): with the choice of the branch of ln(detH(⋅)) on C+ such thatWe also provide some applications in the context of supersymmetric quantum mechanics to zeta function and heat kernel regularized spectral asymmetries and the eta-invariant.  相似文献   

5.
In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces and Triebel–Lizorkin spaces for all s∈(0,1) and p,q∈(n/(n+s),∞], both in Rn and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve on Rn for all s∈(0,1) and q∈(n/(n+s),∞]. A metric measure space version of the above morphism property is also established.  相似文献   

6.
Given a nonempty closed subset A of a Hilbert space X, we denote by L(A) the space of all bounded Lipschitz mappings from A into X, equipped with the supremum norm. We show that there is a continuous mapping Fc:L(A)?L(X) such that for each gL(A), Fc(g)|A=g, , and . We also prove that the corresponding set-valued extension operator is lower semicontinuous.  相似文献   

7.
An identity of the Picone type for higher-order half-linear ordinary differential operators of the form and where pj and Pj, j=0,…,n, are continuous functions defined on [a,b] and , is derived and then the Sturmian comparison theory for the corresponding 2nth-order equations lα[x]=0 and Lα[y]=0 based on this identity is developed.  相似文献   

8.
We consider the following question: given ASL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential qL2([0,2π]) to , the lift to the universal cover of SL(2,R) of the fundamental matrix map ,
  相似文献   

9.
We prove Liouville type theorems for weak solutions of the Navier–Stokes and the Euler equations. In particular, if the pressure satisfies pL1(0,T;L1(RN)) with , then the corresponding velocity should be trivial, namely v=0 on RN×(0,T). In particular, this is the case when pL1(0,T;Hq(RN)), where Hq(RN), q∈(0,1], the Hardy space. On the other hand, we have equipartition of energy over each component, if pL1(0,T;L1(RN)) with . Similar results hold also for the magnetohydrodynamic equations.  相似文献   

10.
In this paper, we prove existence of radially symmetric minimizersuA(x)=UA(|x|), having UA(⋅)AC monotone and increasing, for the convex scalar multiple integral(∗ ) among those u(⋅) in the Sobolev space. Here, |u(x)| is the Euclidean norm of the gradient vector and BR is the ball ; while A is the boundary data.Besides being e.g. superlinear (but no growth needed if (∗) is known to have minimum), our Lagrangian?∗∗:R×R→[0,] is just convex lsc and and ?∗∗(s,⋅) is even; while ρ1(⋅) and ρ2(⋅) are Borel bounded away from .Remarkably, (∗) may also be seen as the calculus of variations reformulation of a distributed-parameter scalar optimal control problem. Indeed, state and gradient pointwise constraints are, in a sense, built-in, since ?∗∗(s,v)= is freely allowed.  相似文献   

11.
The aim of the paper is to generalize the notion of the Haar integral. For a compact semigroup S acting continuously on a Hausdorff compact space Ω, the algebra A(S)⊂C(Ω,R) of S-invariant functions and the linear space M(S) of S-invariant (real-valued) finite signed measures are considered. It is shown that if S has a left and right invariant measure, then the dual space of A(S) is isometrically lattice-isomorphic to M(S) and that there exists a unique linear operator (called the Haar integral) such that for each fA(S) and for any fC(Ω,R) and sS, , where .  相似文献   

12.
Let X,Y,Z be real Hilbert spaces, let f:XR∪{+}, g:YR∪{+} be closed convex functions and let A:XZ, B:YZ be linear continuous operators. Let us consider the constrained minimization problem Given a sequence (γn) which tends toward 0 as n→+, we study the following alternating proximal algorithm where α and ν are positive parameters. It is shown that if the sequence (γn) tends moderately slowly toward 0, then the iterates of (A) weakly converge toward a solution of (P). The study is extended to the setting of maximal monotone operators, for which a general ergodic convergence result is obtained. Applications are given in the area of domain decomposition for PDE’s.  相似文献   

13.
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtxD(B)). For a closed subset ΛR, we prove that the following properties (i) and (ii) are equivalent: (i) for every function fAP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution uAP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λΛ and .  相似文献   

14.
We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], αR, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some KR, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all αR. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
  相似文献   

15.
For a Banach space B and for a class A of its bounded closed retracts, endowed with the Hausdorff metric, we prove that retractions on elements AA can be chosen to depend continuously on A, whenever nonconvexity of each AA is less than . The key geometric argument is that the set of all uniform retractions onto an α-paraconvex set (in the spirit of E. Michael) is -paraconvex subset in the space of continuous mappings of B into itself. For a Hilbert space H the estimate can be improved to and the constant can be replaced by the root of the equation α+α2+α3=1.  相似文献   

16.
We develop a theory of existence, uniqueness and regularity for the following porous medium equation with fractional diffusion, with m>m?=(N−1)/N, N?1 and fL1(RN). An L1-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all xRN, t>0.  相似文献   

17.
We consider non-local linear Schrödinger-type critical systems of the type(1) where Ω is antisymmetric potential in L2(R,so(m)), v is an Rm valued map and Ωv denotes the matrix multiplication. We show that every solution vL2(R,Rm) of (1) is in fact in , for every 2?p<+∞, in other words, we prove that the system (1) which is a-priori only critical in L2 happens to have a subcritical behavior for antisymmetric potentials. As an application we obtain the regularity of weak 1/2-harmonic maps into C2 compact sub-manifolds without boundary.  相似文献   

18.
In this work we consider a nuclear spin generator given by where α, β, κ are nonnegative parameters. It models the two temperature feedback nuclear reactor problem as model by Vreeke and Sandquist (1970) [4]. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. We prove that β=0 or β≠0 and κ=0 are the only values of the parameters for which the system is integrable, and in this case we provide an explicit expression for its first integrals.  相似文献   

19.
In this paper we study the existence of infinitely many homoclinic solutions for second order Hamiltonian systems , , where L(t) is unnecessarily positive definite for all tR, and W(t,u) is of subquadratic growth as |u|→.  相似文献   

20.
Let be identically distributed random vectors in Rd, independently drawn according to some probability density. An observation is said to be a layered nearest neighbour (LNN) of a point if the hyperrectangle defined by and contains no other data points. We first establish consistency results on , the number of LNN of . Then, given a sample of independent identically distributed random vectors from Rd×R, one may estimate the regression function by the LNN estimate , defined as an average over the Yi’s corresponding to those which are LNN of . Under mild conditions on r, we establish the consistency of towards 0 as n, for almost all and all p≥1, and discuss the links between rn and the random forest estimates of Breiman (2001) [8]. We finally show the universal consistency of the bagged (bootstrap-aggregated) nearest neighbour method for regression and classification.  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