Singularly perturbed critical Choquard equations
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In this article, the semiclassical limit for the singularly perturbed Choquard equation with constant coefficients was studied and the existence and multiplicity of semi-classical solutions were established by variational methods.About:
This article is published in Journal of Differential Equations.The article was published on 2017-10-05 and is currently open access. It has received 127 citations till now. The article focuses on the topics: Sobolev inequality & Limit (mathematics).read more
Citations
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Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth
Daniele Cassani,Jianjun Zhang +1 more
TL;DR: In this paper, the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations were studied, where the nonlinearity exhibits critical growth in the sense of the Hardy-Littlewood-Sobolev inequality, in the range of the so-called upper critical exponent.
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Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions
Xianhua Tang,Sitong Chen +1 more
TL;DR: In this paper, the authors considered the singularly perturbed problem with the Berestycki-Lions assumption and showed that the problem admits a semiclassical ground state solution and a ground-state solution under the general "BeneryckiLions" assumptions.
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Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity
TL;DR: In this paper, the authors studied the Riesz potential of the problem with convolutional nonlinearity and showed that the ground state solution admits ground state solutions under mild assumptions on V and f.
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Existence of solutions for critical Choquard equations via the concentration-compactness method
TL;DR: In this article, the authors considered the nonlinear Choquard equation where 0 < μ < N, N ⩾ 3, g(u) is of critical growth due to the Hardy-Littlewood-Sobolev inequality and showed the existence of high energy solution by using a nonlocal version of global compactness lemma.
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Nonlinear Choquard equations: Doubly critical case
TL;DR: It is shown that when F is doubly critical, the nonlinear Choquard equation admits a nontrivial solution if N ≥ 5 and α + 4 N .
References
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Journal ArticleDOI
A relation between pointwise convergence of functions and convergence of functionals
TL;DR: In this article, it was shown that if f n is a sequence of uniformly L p-bounded functions on a measure space, and f n → f pointwise a, then lim for all 0 < p < ∞.
Journal ArticleDOI
On a class of nonlinear Schro¨dinger equations
TL;DR: In this paper, the existence of standing wave solutions of nonlinear Schrodinger equations was studied and sufficient conditions for nontrivial solutionsu ∈W¯¯¯¯1,2(ℝ�姫 n ) were established.
Journal ArticleDOI
Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
TL;DR: In this article, the Hartree-Fock theory of a plasma was used to prove existence and uniqueness of a minimization of the functional function of an electron trapped in its own hole.