Results 11 to 20 of about 109 (104)
Resistance Conditions and Applications
Analysis and Geometry in Metric Spaces, 2013 This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several ...
Kinnunen Juha, Silvestre Pilar
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Advances in Nonlinear Analysis, 2018 We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood ...
Cassani Daniele, Zhang Jianjun
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Existence of positive solutions to negative power nonlinear integral equations with weights
Boundary Value Problems, 2020 This paper is devoted to the existence and non-existence of positive solutions to the following negative power nonlinear integral equation related to the sharp reversed Hardy–Littlewood–Sobolev inequality: f q − 1 ( x ) = ∫ Ω K ( x ) f ( y ) K ( y ) | x −
Hang Chen, Qianqiao Guo, Qian Wang
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On the critical Choquard-Kirchhoff problem on the Heisenberg group
Advances in Nonlinear Analysis, 2022 In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
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Biharmonic system with Hartree-type critical nonlinearity
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this article, we investigate the multiplicity results of the following biharmonic Choquard system involving critical nonlinearities with sign-changing weight function: \begin{align*} \begin{cases} \Delta^{2}u = \lambda F(x) |u|^{r-2}u+ H(x)\left ...
Anu Rani, Sarika Goyal
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Abstract and Applied Analysis, 2014 We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and ...
Linfen Cao, Zhaohui Dai
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Ground state solutions for nonlinearly coupled systems of Choquard type with lower critical exponent
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper, we study the existence of ground state solutions for the following nonlinearly coupled systems of Choquard type with lower critical exponent by variational methods \begin{equation*} \begin{cases} \displaystyle-\Delta u+V(x)u=(I_\alpha\ast ...
Anran Li, Peiting Wang, Chongqing Wei
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Advances in Nonlinear Analysis, 2021 We are concerned with a class of Choquard type equations with weighted potentials and Hardy–Littlewood–Sobolev lower critical ...
Zhou Shuai, Liu Zhisu, Zhang Jianjun
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On the stability of a version of nonlocal Sobolev inequality
Bulletin of Mathematical SciencesIn this paper, we investigate the stability of the corresponding nonlocal Sobolev inequality ∫ℝN|Δu|2dx≥S∗∫ℝN(|x|−α∗|u|p)updx1p,∀u∈𝒟2,2(ℝN), where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the best constant.
Weiwei Ye, Xinyun Zhang
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Solutions with prescribed mass for a critical Choquard equation driven by a local-nonlocal operator [PDF]
Opuscula MathematicaIn this paper, we study the normalized solutions of the following critical growth Choquard equation with mixed local and nonlocal operators: \[\begin{split}-\Delta u +(-\Delta)^s u &= \lambda u +\mu |u|^{p-2}u +(I_{\alpha}*|u|^{2^*_{\alpha}})|u|^{2^*_ ...
Nidhi Nidhi, Konijeti Sreenadh
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