共查询到20条相似文献,搜索用时 31 毫秒
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By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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The paper deals with the radially symmetric solutions of ut=Δu+um(x,t)vn(0,t), vt=Δv+up(0,t)vq(x,t), subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that u (v) blows up alone if and only if m>p+1 (q>n+1), which means that any blow-up is simultaneous if and only if m≤p+1, q≤n+1. (ii) Any blow-up is u (v) blowing up with v (u) remaining bounded if and only if m>p+1, q≤n+1 (m≤p+1, q>n+1). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if m>p+1, q>n+1. Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. 相似文献
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We show that the equality m1(f(x))=m2(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps, f(a)=g(a)=0 and m1,m2 are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. 相似文献
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In an earlier publication a linear operator THar was defined as an unusual self-adjoint extension generated by each linear elliptic partial differential expression, satisfying suitable conditions on a bounded region Ω of some Euclidean space. In this present work the authors define an extensive class of THar-like self-adjoint operators on the Hilbert function space L2(Ω); but here for brevity we restrict the development to the classical Laplacian differential expression, with Ω now the planar unit disk. It is demonstrated that there exists a non-denumerable set of such THar-like operators (each a self-adjoint extension generated by the Laplacian), each of which has a domain in L2(Ω) that does not lie within the usual Sobolev Hilbert function space W2(Ω). These THar-like operators cannot be specified by conventional differential boundary conditions on the boundary of ∂Ω, and may have non-empty essential spectra. 相似文献
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In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
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We study a family of differential operators Lα in two variables, depending on the coupling parameter α?0 that appears only in the boundary conditions. Our main concern is the spectral properties of Lα, which turn out to be quite different for α<1 and for α>1. In particular, Lα has a unique self-adjoint realization for α<1 and many such realizations for α>1. In the more difficult case α>1 an analysis of non-elliptic pseudodifferential operators in dimension one is involved. 相似文献
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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We prove that, unless assuming additional set theoretical axioms, there are no reflexive spaces without unconditional sequences of the density continuum. We show that for every integer n there are normalized weakly-null sequences of length ωn without unconditional subsequences. This together with a result of Dodos et al. (2011) [7] shows that ωω is the minimal cardinal κ that could possibly have the property that every weakly null κ-sequence has an infinite unconditional basic subsequence. We also prove that for every cardinal number κ which is smaller than the first ω-Erd?s cardinal there is a normalized weakly-null sequence without subsymmetric subsequences. Finally, we prove that mixed Tsirelson spaces of uncountable densities must always contain isomorphic copies of either c0 or ?p, with p≥1. 相似文献
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Mehmet Özer Yasar Polatoglu Gürsel Hacibekiroglou Antonios Valaristos Amalia N. Miliou Antonios N. Anagnostopoulos Antanas Čenys 《Nonlinear Analysis: Theory, Methods & Applications》2008
The dynamic behaviour of the one-dimensional family of maps f(x)=c2[(a−1)x+c1]−λ/(α−1) is examined, for representative values of the control parameters a,c1, c2 and λ. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a. The maps f(x) are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an xn versus λ plot, an initial exponential decay followed by a bifurcation. The value of λ at which this bifurcation takes place depends on the values of the parameters a,c1 and c2. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x) undergoing a period doubling. For values of a higher than 1 and at higher values of λ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter c1 between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to pc with an inverse power, λ, of the distance to the origin. Assuming the existence of critical exponents (as is known in the case of the triangular site lattice) if the power is less than 1/ν, with ν the correlation length exponent, we demonstrate an infinite cluster with scale dimension given by DH=2−βλ. Further, we investigate the critical case λc=1/ν and show that iterated logarithmic corrections will tip the balance between the possibility and impossibility of an infinite cluster. 相似文献
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For α∈R, let pR(t,x,x) denote the diagonal of the transition density of the α-Bessel process in (0,1], killed at 0 and reflected at 1. As a function of x, if either α≥3 or α=1, then for t>0, the diagonal is nondecreasing. This monotonicity property fails if 1≠α<3. 相似文献
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Let T be a tree with s ends and f,g be continuous maps from T to T with f°g=g°f. In this note we show that if there exists a positive integer m≥2 such that gcd(m,l)=1 for any 2≤l≤s and f,g share a periodic point which is a km-periodic point of f for some positive integer k, then the topological entropy of f°g is positive. 相似文献
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