On the brezis-nirenberg problem in a ball
WebThe Brezis-Nirenberg problem with Hartree type nonlinearities was also investigated. In this regard Gao and Yang in [10] established some existence results for a class of … Web1 de jul. de 2024 · Semantic Scholar extracted view of "The Brezis–Nirenberg problem for the Laplacian with a singular drift in Rn and Sn" by R. Benguria et al. Skip to search ... We consider the following superlinear elliptic equation on S n where D is a geodesic ball on S n with geodesic radius θ1, and Δ S n is the Laplace–Beltrami operator on S ...
On the brezis-nirenberg problem in a ball
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Web16 de abr. de 2024 · The main purpose of this paper is to establish the existence, nonexistence and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg … WebTHE BREZIS-NIRENBERG PROBLEM ALESSANDRO IACOPETTI Abstract. We study the asymptotic behavior, as λ → 0, of least energy radial sign-changing solutions uλ, of the Brezis-Nirenberg problem (−∆u = λu + u 2∗−2u in B1 u = 0 on ∂B1, where λ > 0, 2∗ = 2n n−2 and B1 is the unit ball of Rn, n ≥ 7.
Web开馆时间：周一至周日7:00-22:30 周五 7:00-12:00; 我的图书馆 WebAbstract We study the following Brezis-Nirenberg type critical exponent problem: {−Δu= λuq +u2∗−1 in BR, u >0 in BR, u= 0 on ∂BR, { − Δ u = λ u q + u 2 ∗ − 1 in B R, u > 0 in B R, u = 0 on ∂ B R, where BR B R is a ball with radius R R in RN(N ≥3) R N ( N ≥ 3), λ >0 λ > …
WebWe study the following Brezis-Nirenberg type critical exponent problem: $$ \begin{cases}-\Delta u = \lambda u^q+ u^{2^{\ast}-1}\,\,\,\hbox{in} \,\,B_R,\\ u > 0\,\,\,\hbox{in}\,\, … Web6 de mar. de 2024 · has at least k positive solutions with s bumps.. A couple of remarks regarding Theorem 1.1 are in order.. Remark 1.1 (1) For the precise meaning of “s bumps”, refer to the proof of Theorem 1.1 in Sect. 7.Roughly speaking, we say a solution has s bumps if most of its mass is concentrated in s disjoint regions. Since the number of …
Web11 de mar. de 2016 · On fractional Schrodinger equations Part III. Nonlocal Critical Problems: 14. The Brezis-Nirenberg result for the fractional Laplacian 15. Generalizations of the Brezis-Nirenberg result 16. The Brezis-Nirenberg result in low dimension 17. The critical equation in the resonant case 18. The Brezis-Nirenberg result for a general …
Web30 de abr. de 2024 · In this paper we discuss the existence and non-existence of weak solutions to parametric fractional equations involving the square root of the Laplacian A 1 / 2 in a smooth bounded domain Ω ⊂ R n ( n ≥ 2) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation. { A 1 / 2 u = λ f ( u) u = 0 … daily maverick tamar ronWebThe Brezis-Nirenberg problem with Hartree type nonlinearities was also investigated. In this regard Gao and Yang in [10] established some existence results for a class of Choquard with Dirichlet boundary conditions. Moreover, in [14], authors studied the nonlocal counterpart of this problem and obtained various results such as existence, daily maverick press readerWeb4 de abr. de 2016 · We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation. -\Delta u. =\left (\int_ {\Omega}\frac { u ^ … biological hierarchy of organismsWebFor positive radial solutions of this problem in a (unit) ball, one is led to an ODE that still makes sense when n is a real number rather than a natural number. Precisely this problem with 2 n 4, was considered by E. Jannelli, The role played by space dimension in elliptic critical problems,J.Di↵erential Equations, 156 (1999), pp. 407–426. daily-max batteryWebarXiv:2111.13417v1 [math.AP] 26 Nov 2024 CRITICAL FUNCTIONS AND BLOW-UP ASYMPTOTICS FOR THE FRACTIONAL BREZIS–NIRENBERG PROBLEM IN LOW … daily maverick zapiro todayWeb10 de jun. de 2024 · On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension. F. Faraci, K. Silva. The present paper deals with a parametrized Kirchhoff type problem involving a critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect of a subcritical perturbation by ... biological hierarchy 意味WebWe consider the Brezis--Nirenberg problem for the Laplacian with a singular drift for a (geodesic) ball in both $\mathbb{R}^{n}$ and $\mathbb{S}^n$, $3 \le n \le 5$. The singular drift we consider derives from a potential which is symmetric around the center of the (geodesic) ball. Here the potential is given by a parameter ($\delta$ say) times the … biological hindi