共查询到20条相似文献,搜索用时 15 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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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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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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Let be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ?Ω. We show that the solution to the linear first-order system:(1) vanishes if and . In particular, square-integrable solutions ζ of (1) with vanish. As a consequence, we prove that: is a norm if with , for some with as well as . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let , , satisfy for some with . Then there exists a constant translation vector and a constant skew-symmetric matrix , such that . 相似文献
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Let and Ω be a bounded Lipschitz domain in . Assume that and the function is non-negative, where ?Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ?Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation in Ω with boundary data , respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) for any given . 相似文献
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Petru Mironescu 《Comptes Rendus Mathematique》2010,348(13-14):743-746
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In this paper, we consider the following elliptic equation(0.1) where , , is differentiable in and is a given nonnegative Hölder continuous function in . The asymptotic behavior at infinity and structure of separation property of positive radial solutions with different initial data for (0.1) are discussed. Moreover, the existence and separation property of infinitely many positive solutions for Hardy equation and an equation related to Caffarelli–Kohn–Nirenberg inequality are obtained respectively, as special cases. 相似文献
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Soojung Kim 《Journal of Differential Equations》2018,264(3):1613-1660
We study viscosity solutions to degenerate and singular elliptic equations of p-Laplacian type on Riemannian manifolds, where an even function is supposed to be strictly convex on . Under the assumption that either or its convex conjugate with some structural condition, we establish a (locally) uniform ABP type estimate and the Krylov–Safonov type Harnack inequality on Riemannian manifolds with the use of an intrinsic geometric quantity to the operator. Here, the -regularities of F and account for degenerate and singular operators, respectively. 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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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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Nguyen Tien Tai 《Journal of Differential Equations》2018,264(6):3940-3975
Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive -solutions of in , where and p is bounded from below by the sixth-order Joseph–Lundgren exponent. Following the main work of Winkler, we introduce the sub- and super-solution method and comparison principle to conclude the asymptotic behavior of solutions. 相似文献
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Existence of standing waves of nonlinear Schrödinger equations with potentials vanishing at infinity
Ohsang Kwon 《Journal of Mathematical Analysis and Applications》2012,387(2):920-930
For a singularly perturbed nonlinear elliptic equation , , we prove the existence of bump solutions concentrating around positive critical points of V when nonnegative V is not identically zero for or nonnegative V satisfies for . 相似文献
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