共查询到20条相似文献,搜索用时 15 毫秒
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Zhichun Zhai 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2611-2630
Let be the space of solutions to the parabolic equation having finite norm. We characterize nonnegative Radon measures μ on having the property , 1≤p≤q<∞, whenever . Meanwhile, denoting by v(t,x) the solution of the above equation with Cauchy data v0(x), we characterize nonnegative Radon measures μ on satisfying , β∈(0,n), p∈[1,n/β], q∈(0,∞). Moreover, we obtain the decay of v(t,x), an isocapacitary inequality and a trace inequality. 相似文献
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Let s∈R. In this paper, the authors first establish the maximal function characterizations of the Besov-type space with and τ∈[0,∞), the Triebel-Lizorkin-type space with p∈(0,∞), q∈(0,∞] and τ∈[0,∞), the Besov-Hausdorff space with p∈(1,∞), q∈[1,∞) and and the Triebel-Lizorkin-Hausdorff space with and , where t′ denotes the conjugate index of t∈[1,∞]. Using this characterization, the authors further obtain the local mean characterizations of these function spaces via functions satisfying the Tauberian condition and establish a Fourier multiplier theorem on these spaces. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking τ=0 and are also new even for Q spaces and Hardy-Hausdorff spaces. 相似文献
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Zhijun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3348-3363
In this paper, we study the boundary behavior of solutions to boundary blow-up elliptic problems , where Ω is a bounded domain with smooth boundary in RN, q>0, , which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary, and f is rapidly varying or normalized regularly varying at infinity. 相似文献
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Tomasz Piasecki 《Journal of Differential Equations》2010,248(8):2171-2198
We investigate a steady flow of a viscous compressible fluid with inflow boundary condition on the density and inhomogeneous slip boundary conditions on the velocity in a cylindrical domain Ω=Ω0×(0,L)∈R3. We show existence of a solution , p>3, where v is the velocity of the fluid and ρ is the density, that is a small perturbation of a constant flow (, ). We also show that this solution is unique in a class of small perturbations of . The term u⋅∇w in the continuity equation makes it impossible to show the existence applying directly a fixed point method. Thus in order to show existence of the solution we construct a sequence (vn,ρn) that is bounded in and satisfies the Cauchy condition in a larger space L∞(0,L;L2(Ω0)) what enables us to deduce that the weak limit of a subsequence of (vn,ρn) is in fact a strong solution to our problem. 相似文献
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Wolfgang Reichel 《Journal of Differential Equations》2010,248(7):1866-680
We consider the 2m-th order elliptic boundary value problem Lu=f(x,u) on a bounded smooth domain Ω⊂RN with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic linear operator of order 2m whose principle part is of the form . We assume that f is superlinear at the origin and satisfies , , where are positive functions and q>1 is subcritical. By combining degree theory with new and recently established a priori estimates, we prove the existence of a nontrivial solution. 相似文献
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We consider the first initial boundary value problem for the non-autonomous nonclassical diffusion equation ut−εΔut−Δu+f(u)=g(t), ε∈[0,1], in a bounded domain in RN. Under a Sobolev growth rate of the nonlinearity f and a suitable exponential growth of the external force g, using the asymptotic a priori estimate method, we prove the existence of pullback D-attractors in the space and the upper semicontinuity of at ε=0. 相似文献
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Biagio Ricceri 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4151-4157
If X is a real Banach space, we denote by WX the class of all functionals possessing the following property: if {un} is a sequence in X converging weakly to u∈X and lim infn→∞Φ(un)≤Φ(u), then {un} has a subsequence converging strongly to u.In this paper, we prove the following result:Let X be a separable and reflexive real Banach space; an interval; a sequentially weakly lower semicontinuous C1 functional, belonging to WX, bounded on each bounded subset of X and whose derivative admits a continuous inverse on X∗; a C1 functional with compact derivative. Assume that, for each λ∈I, the functional Φ−λJ is coercive and has a strict local, not global minimum, say .Then, for each compact interval [a,b]⊆I for which , there exists r>0 with the following property: for every λ∈[a,b] and every C1 functional with compact derivative, there exists δ>0 such that, for each μ∈[0,δ], the equation
Φ′(x)=λJ′(x)+μΨ′(x) 相似文献
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Ryuji Kajikiya 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2117-2131
In this paper, a superlinear elliptic equation whose coefficient diverges on the boundary is studied in any bounded domain Ω under the zero Dirichlet boundary condition. Although the equation has a singularity on the boundary, a solution is smooth on the closure of the domain. Indeed, it is proved that the problem has a positive solution and infinitely many solutions without positivity, which belong to or . Moreover, it is proved that a positive solution has a higher order regularity up to . 相似文献
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Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:
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Yasuhito Miyamoto 《Journal of Differential Equations》2010,249(8):1853-1870
Let (n?3) be a ball, and let f∈C3. We are concerned with the Neumann problem
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Guilong Gui 《Advances in Mathematics》2010,225(3):1248-1284
In this paper, we consider the stability to the global large solutions of 3-D incompressible Navier-Stokes equations in the anisotropic Sobolev spaces. In particular, we proved that for any , given a global large solution v∈C([0,∞);H0,s0(R3)∩L3(R3)) of (1.1) with and a divergence free vector satisfying for some sufficiently small constant depending on , v, and , (1.1) supplemented with initial data v(0)+w0 has a unique global solution in u∈C([0,∞);H0,s0(R3)) with ∇u∈L2(R+,H0,s0(R3)). Furthermore, uh is close enough to vh in C([0,∞);H0,s(R3)). 相似文献
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Let Ω⊂R4 be a smooth oriented bounded domain, be the Sobolev space, and be the first eigenvalue of the bi-Laplacian operator Δ2. Then for any α: 0?α<λ(Ω), we have
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Xianling Fan 《Journal of Mathematical Analysis and Applications》2009,349(2):436-442
Consider the eigenvalue problem : −Δu=λf(x,u) in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN. Denote by the set of all Carathéodory functions f:Ω×R→R such that for a.e. x∈Ω, f(x,⋅) is Lipschitzian with Lipschitz constant L, f(x,0)=0 and , and denote by (resp. ) the set of λ>0 such that has at least one nonzero classical (resp. weak) solution. Let λ1 be the first eigenvalue for the Laplacian-Dirichlet problem. We prove that and . Our result is a positive answer to Ricceri's conjecture if use f(x,u) instead of f(u) in the conjecture. 相似文献