共查询到20条相似文献,搜索用时 31 毫秒
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The following equation d2/dt2(x(t)+px(t-1))=qx(2[(t+1)/2])+f(t) is considered and necessary and sufficient conditions are given in order to ensure the existence and uniqueness of pseudo almost periodic solutions. 相似文献
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We prove that the solution map of the two-component Camassa–Holm system is not uniformly continuous as a map from a bounded subset of the Sobolev space Hs(T)×Hr(T) to C([0,1],Hs(T)×Hr(T)) when s?1 and r?0. We also demonstrate the nonuniform continuous property in the continuous function space C1(T)×C1(T). 相似文献
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This paper is concerned with special regularity properties of the solutions to the Maxwell–Landau–Lifshitz (MLL) system describing ferromagnetic medium. Besides the classical results on the boundedness of ∂tm,∂tE and ∂tH in the spaces L∞(I,L2(Ω)) and L2(I,W1,2(Ω)) we derive also estimates in weighted Sobolev spaces. This kind of estimates can be used to control the Taylor remainder when estimating the error of a numerical scheme. 相似文献
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An exact finite-difference scheme for a system of two linear differential equations with constant coefficients, (d/dt)x(t)=Ax(t), is proposed. The scheme is different from what was proposed by Mickens [Nonstandard Finite Difference Models of Differential Equations, World Scientific, New Jersey, 1994, p. 147], in which the derivatives of the two equations are formed differently. Our exact scheme is in the form of (1/φ(h))(xk+1-xk)=A[θxk+1+(1-θ)xk]; both derivatives are in the same form of (xk+1-xk)/φ(h). 相似文献
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Cristian Enache 《Comptes Rendus Mathematique》2014,352(1):37-42
In this note we derive a maximum principle for an appropriate functional combination of u(x) and |∇u|2, where u(x) is a strictly convex classical solution to a general class of Monge–Ampère equations. This maximum principle is then employed to establish some isoperimetric inequalities of interest in the theory of surfaces of constant Gauss curvature in RN+1. 相似文献
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We study the existence of solutions u:R3→R2 for the semilinear elliptic systems where W:R2→R is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima a± of W, that (0.1) has infinitely many geometrically distinct solutions u∈C2(R3,R2) which satisfy u(x,y,z)→a± as x→±∞ uniformly with respect to (y,z)∈R2 and which exhibit dihedral symmetries with respect to the variables y and z . We also characterize the asymptotic behavior of these solutions as |(y,z)|→+∞. 相似文献
equation(0.1)
−Δu(x,y,z)+∇W(u(x,y,z))=0,
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Denote by gdist(p) the least non-zero number of cells that have to be changed to get a latin square from the table of addition modulo p . A conjecture of Drápal, Cavenagh and Wanless states that there exists c>0 such that gdist(p)?clog(p). In this paper the conjecture is proved for c≈7.21, and as an intermediate result it is shown that an equilateral triangle of side n can be non-trivially dissected into at most 5log2(n) integer-sided equilateral triangles. The paper also presents some evidence which suggests that gdist(p)/log(p)≈3.56 for large values of p. 相似文献
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Let R=(-∞,∞) and let Q∈C2:R→R+=[0,∞) be an even function. Then in this paper we consider the infinite–finite range inequality, an estimate for the Christoffel function, and the Markov–Bernstein inequality with the exponential weights wρ(x)=|x|ρe-Q(x),x∈R. 相似文献
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We prove Liouville type results for non-negative solutions of the differential inequality Δφu?f(u)?(|∇0u|) on the Heisenberg group under a generalized Keller–Osserman condition. The operator Δφu is the φ -Laplacian defined by div0(|∇0u|−1φ(|∇0u|)∇0u) and φ, f and ? satisfy mild structural conditions. In particular, ? is allowed to vanish at the origin. A key tool that can be of independent interest is a strong maximum principle for solutions of such differential inequality. 相似文献
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