共查询到20条相似文献,搜索用时 31 毫秒
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《Discrete Mathematics》2022,345(4):112754
Motivated by the application to three-dimensional optical orthogonal codes, we consider the construction for a w-cyclic holey group divisible packing of type with block size three (3-HGDP for short). A maximum w-cyclic 3-HGDP of type contains the largest possible number of base blocks. When , the exact size of maximum w-cyclic 3-HGDP of type has been determined in our previous work. Based on recursive constructions, in this paper we establish a framework to construct maximum w-cyclic 3-HGDPs of type where (mod 3). In the process, direct constructions on several key auxiliary designs are displayed by choosing appropriate automorphism groups. Eventually, the sizes of maximum w-cyclic 3-HGDPs of type are determined for all positive integers and w, only leaving a small fraction of possible exceptions unresolved. Furthermore, application of our results to three-dimensional optical orthogonal codes is presented. 相似文献
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Teresa DAprile 《Journal of Differential Equations》2019,266(11):7379-7415
We are concerned with the existence of blowing-up solutions to the following boundary value problem where Ω is a smooth and bounded domain in such that , is a positive smooth function, N is a positive integer and is a small parameter. Here defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution blowing up at 0 and satisfying as . 相似文献
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In this paper we study the following type of the Schrödinger–Poisson–Slater equation with critical growth where and . For the case of . We develop a novel perturbation approach, together with the well-known Mountion–Pass theorem, to prove the existence of positive ground states. For the case of , we obtain the nonexistence of nontrivial solutions by restricting the range of μ and also study the existence of positive solutions by the constrained minimization method. For the case of , we use a truncation technique developed by Brezis and Oswald [9] together with a measure representation concentration-compactness principle due to Lions [27] to prove the existence of radial symmetrical positive solutions for with some . The above results nontrivially extend some theorems on the subcritical case obtained by Ianni and Ruiz [18] to the critical case. 相似文献
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Xiangqing Liu Junfang Zhao Jiaquan Liu 《Journal of Mathematical Analysis and Applications》2019,469(1):220-238
Consider the critical p-Laplacian equation in where , is the critical exponent of the Sobolev imbedding from to , and is the p-Laplacian operator, . We prove polynomial decay of the solutions The decay exponent is the best possible. 相似文献
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We consider the nonlinear problem of inhomogeneous Allen–Cahn equation where Ω is a bounded domain in with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on . Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional . We can prove that there exists a solution such that: as , approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ. 相似文献
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This paper deals with positive solutions of the fully parabolic system under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain with positive parameters and nonnegative smooth initial data .Global existence and boundedness of solutions were shown if in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying . This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in . 相似文献
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Let () be a bounded domain and . Put with . In this paper, we provide various necessary and sufficient conditions for the existence of weak solutions to where , , τ and ν are measures on Ω and ?Ω respectively. We then establish existence results for the system where , , , τ and are measures on Ω, ν and are measures on ?Ω. We also deal with elliptic systems where the nonlinearities are more general. 相似文献
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Michael Winkler 《Journal of Functional Analysis》2019,276(5):1339-1401
The Keller–Segel–Navier–Stokes system
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is considered in a bounded convex domain with smooth boundary, where and , and where and are given parameters.It is proved that under the assumption that be finite, for any sufficiently regular initial data satisfying and , the initial-value problem for (?) under no-flux boundary conditions for n and c and homogeneous Dirichlet boundary conditions for u possesses at least one globally defined solution in an appropriate generalized sense, and that this solution is uniformly bounded in with respect to the norm in .Moreover, under the explicit hypothesis that , these solutions are shown to stabilize toward a spatially homogeneous state in their first two components by satisfying Finally, under an additional condition on temporal decay of f it is shown that also the third solution component equilibrates in that in as . 相似文献
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Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
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Fengping Yao 《Journal of Differential Equations》2019,266(4):2078-2099
In this paper we obtain the following local Lorentz estimates of the weak solutions for a class of quasilinear parabolic systems where for . 相似文献
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In this paper, we investigate the following modified nonlinear fourth-order elliptic equations where is the biharmonic operator, V is an indefinite potential, g grows subcritically and satisfies the Ambrosetti-Rabinowitz type condition with . Using Morse theory, we obtain nontrivial solutions of the above equations. Our result complements recent results in [17], where g has to be 3-superlinear at infinity. 相似文献
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Ryosuke Hyakuna 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(4):1081-1104
This paper is concerned with the Cauchy problem for the Hartree equation on with the nonlinearity of type . It is shown that a global solution with some twisted persistence property exists for data in the space under some suitable conditions on γ and spatial dimension . It is also shown that the global solution u has a smoothing effect in terms of spatial integrability in the sense that the map is well defined and continuous from to , which is well known for the solution to the corresponding linear Schrödinger equation. Local and global well-posedness results for hat -spaces are also presented. The local and global results are proved by combining arguments by Carles–Mouzaoui with a new functional framework introduced by Zhou. Furthermore, it is also shown that the global results can be improved via generalized dispersive estimates in the case of one space dimension. 相似文献
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Yuchen Ding 《Comptes Rendus Mathematique》2019,357(6):483-486
Assuming the abc conjecture, Silverman proved that, for any given positive integer , there are primes such that . In this paper, we show that, for any given integers and , there still are primes satisfying and , under the assumption of the abc conjecture. This improves a recent result of Chen and Ding. 相似文献