共查询到20条相似文献,搜索用时 29 毫秒
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Quốc Anh Ngô 《Comptes Rendus Mathematique》2017,355(5):526-532
In this note, we mainly study the relation between the sign of and in with and for . Given the differential inequality , first we provide several sufficient conditions so that holds. Then we provide conditions such that for all , which is known as the sub poly-harmonic property for u. In the last part of the note, we revisit the super poly-harmonic property for solutions to and with in . 相似文献
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This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
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Tristan Roy 《Journal of Differential Equations》2018,264(9):6013-6024
The purpose of this corrigendum is to point out some errors that appear in [1]. Our main result remains valid, i.e scattering of solutions of the loglog energy-supercritical Schrödinger equation , , , with , radial data but with slightly different values of , i.e if and if . We propose some corrections. 相似文献
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《Journal of Mathematical Analysis and Applications》2014,419(2):783-795
We study restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the Stein–Tomas restriction result can be improved to the estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in dimensions. 相似文献
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《Journal de Mathématiques Pures et Appliquées》2012,97(6):527-554
This paper deals with the Klein–Gordon equation on the Poincaré chart of the 5-dimensional Anti-de Sitter universe. When the mass μ is larger than , the Cauchy problem is well-posed despite the loss of global hyperbolicity due to the time-like horizon. We express the finite energy solutions in the form of a continuous Kaluza–Klein tower and we deduce a uniform decay as . We investigate the case , , which encompasses the gravitational fluctuations, , and the electromagnetic waves, . The propagation of the wave front set shows that the horizon acts like a perfect mirror. We establish that the smooth solutions decay as , and we get global estimates of Strichartz type. When ν is even, there appears a lacuna and the equipartition of the energy occurs at finite time for the compactly supported initial data, although the Huygens principle fails. We address the cosmological model of the negative-tension Minkowski brane, on which a Robin boundary condition is imposed. We prove the hyperbolic mixed problem is well-posed and the normalizable solutions can be expanded into a discrete Kaluza–Klein tower. We establish some estimates in suitable weighted Sobolev spaces. 相似文献
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In a previous work, it was shown how the linearized strain tensor field can be considered as the sole unknown in the Neumann problem of linearized elasticity posed over a domain , instead of the displacement vector field in the usual approach. The purpose of this Note is to show that the same approach applies as well to the Dirichlet–Neumann problem. To this end, we show how the boundary condition on a portion of the boundary of Ω can be recast, again as boundary conditions on , but this time expressed only in terms of the new unknown . 相似文献
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In this paper, we study the following fractional Kirchhoff equations where are constants, and is the fractional Laplacian operator with , , , is real parameter. is the critical Sobolev exponent. g satisfies the Berestycki–Lions-type condition (see [2]). By using Poho?aev identity and concentration-compact theory, we show that the above problem has at least one nontrivial solution. Furthermore, the phenomenon of concentration of solutions is also explored. Our result supplements the results of Lü (see [8]) concerning the Hartree-type nonlinearity with . 相似文献
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Daniela Giachetti Pedro J. Martínez-Aparicio François Murat 《Journal of Functional Analysis》2018,274(6):1747-1789
In the present paper we perform the homogenization of the semilinear elliptic problem In this problem is a Carathéodory function such that a.e. for every , with h in some and Γ a function such that and for every . On the other hand the open sets are obtained by removing many small holes from a fixed open set Ω in such a way that a “strange term” appears in the limit equation in the case where the function depends only on x.We already treated this problem in the case of a “mild singularity”, namely in the case where the function satisfies . In this case the solution to the problem belongs to and its definition is a “natural” and rather usual one.In the general case where exhibits a “strong singularity” at , which is the purpose of the present paper, the solution to the problem only belongs to but in general does not belong to anymore, even if vanishes on in some sense. Therefore we introduced a new notion of solution (in the spirit of the solutions defined by transposition) for problems with a strong singularity. This definition allowed us to obtain existence, stability and uniqueness results.In the present paper, using this definition, we perform the homogenization of the above semilinear problem and we prove that in the homogenized problem, the “strange term” still appears in the left-hand side while the source term is not modified in the right-hand side. 相似文献
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Roberta Filippucci Patrizia Pucci Frédéric Robert 《Journal de Mathématiques Pures et Appliquées》2009,91(2):156-177
Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that admits a positive weak solution in of class , whenever , and . The technique is based on the existence of extremals of some Hardy–Sobolev type embeddings of independent interest. We also show that if is a weak solution in of , then when either , or and u is also of class . 相似文献
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This paper investigates the existence and asymptotic behavior of nodal solutions to the following gauged nonlinear Schrödinger equation where , and is the so-called Chern–Simons term. We prove that for any positive integer k, the problem has a sign-changing solution which changes sign exactly k times. Moreover, the energy of is strictly increasing in k, and for any sequence , there exists a subsequence , such that converges in to as , where also changes sign exactly k times and solves the following equation 相似文献
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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