共查询到20条相似文献,搜索用时 31 毫秒
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This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
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Pavle V.M. Blagojević Aleksandra Dimitrijević Blagojević Ljubiša D.R. Kočinac 《Topology and its Applications》2013
In this paper we give the complete answer to a question posed by A. Arhangel?skii and prove that the sphere Sn is diagonal resolvable if and only if Sn is an H -space if and only if n∈{0,1,3,7}. Moreover, we prove that any upper half even dimensional Q-sphere cannot be diagonal resolvable. 相似文献
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We show that for any δ∈[0,1) there exists a homogeneous order 2−δ analytic outside zero solution to a uniformly elliptic Hessian equation in R5. 相似文献
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In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q∈L1[0,1] and qn=0 for n=0,−1,−2,..., where qn are the Fourier coefficients of q with respect to the system {ei2πnx}. We prove that the Bloch eigenvalues are (2πn+t)2 for n∈Z, t∈C and find explicit formulas for the Bloch functions. Then we consider the inverse problem for this operator. 相似文献
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We study the regularity up to the boundary of solutions to the Dirichlet problem for the fractional Laplacian. We prove that if u is a solution of (−Δ)su=g in Ω , u≡0 in Rn\Ω, for some s∈(0,1) and g∈L∞(Ω), then u is Cs(Rn) and u/δs|Ω is Cα up to the boundary ∂Ω for some α∈(0,1), where δ(x)=dist(x,∂Ω). For this, we develop a fractional analog of the Krylov boundary Harnack method. 相似文献
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Dongwen Qi 《Expositiones Mathematicae》2009,27(1):87-91
A new proof is given for the statement: For an irreducible, infinite Coxeter group (W,S) and w∈W, if wSw-1=S, then w=1 (the identity element of W). 相似文献
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We study the problem (−Δ)su=λeu in a bounded domain Ω⊂Rn, where λ is a positive parameter. More precisely, we study the regularity of the extremal solution to this problem. Our main result yields the boundedness of the extremal solution in dimensions n≤7 for all s∈(0,1) whenever Ω is, for every i=1,...,n, convex in the xi-direction and symmetric with respect to {xi=0}. The same holds if n=8 and s?0.28206..., or if n=9 and s?0.63237.... These results are new even in the unit ball Ω=B1. 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 present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α<1/2) dissipation α(−Δ): If a Leray–Hopf weak solution is Hölder continuous θ∈Cδ(R2) with δ>1−2α on the time interval [t0,t], then it is actually a classical solution on (t0,t]. 相似文献
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Using best interpolation function based on a given function information, we present a best quadrature rule of function on Sobolev class KWr[-1,1] with Chebyshev weight. The given function information means that the values of a function f∈KWr[-1,1] and its derivatives up to r-1 order at a set of nodes x are given. Error bounds are obtained, and the method is illustrated by some examples. 相似文献
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For an algebraically closed field F, we show that any matrix polynomial P(λ)∈F[λ]n×m, n?m, can be reduced to triangular form, preserving the degree and the finite and infinite elementary divisors. We also characterize the real matrix polynomials that are triangularizable over the real numbers and show that those that are not triangularizable are quasi-triangularizable with diagonal blocks of sizes 1×1 and 2×2. The proofs we present solve the structured inverse problem of building up triangular matrix polynomials starting from lists of elementary divisors. 相似文献
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In this paper the question of finding infinitely many solutions to the problem −Δu+a(x)u=|u|p−2u, in RN, u∈H1(RN), is considered when N≥2, p∈(2,2N/(N−2)), and the potential a(x) is a positive function which is not required to enjoy symmetry properties. Assuming that a(x) satisfies a suitable “slow decay at infinity” condition and, moreover, that its graph has some “dips”, we prove that the problem admits either infinitely many nodal solutions or infinitely many constant sign solutions. The proof method is purely variational and allows to describe the shape of the solutions. 相似文献
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Rolci Cipolatti Flávio Dickstein Jean-Pierre Puel 《Journal of Mathematical Analysis and Applications》2015
We study the existence of standing wave solutions of the complex Ginzburg–Landau equation in RN, where α>0, (N−2)α<4, ρ>0 and θ,γ∈R. We show that for any θ∈(−π/2,π/2) there exists ε>0 such that (GL) has a non-trivial standing wave solution if |γ−θ|<ε. Analogous result is obtained in a ball Ω∈RN for ρ>−λ1, where λ1 is the first eigenvalue of the Laplace operator with Dirichlet boundary conditions. 相似文献
equation(GL)
φt−eiθ(ρI−Δ)φ−eiγ|φ|αφ=0
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In this paper, we give a new proof of a result of R. Jones showing almost everywhere convergence of spherical means of actions of Rd on Lp(X)-spaces are convergent for d?3 and p>d/(d-1). 相似文献
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In this paper, we give some necessary and sufficient conditions for the existence of Re-nnd and nonnegative definite {1,3}- and {1,4}-inverses of a matrix A∈Cn×n and completely described these sets. Moreover, we prove that the existence of nonnegative definite {1,3}-inverse of a matrix A is equivalent with the existence of its nonnegative definite {1,2,3}-inverse and present the necessary and sufficient conditions for the existence of Re-nnd {1,3,4}-inverse of A. 相似文献