Positive and sign changing solutions to a nonlinear Choquard equation
Mónica Clapp,Dora Salazar +1 more
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TLDR
In this paper, the authors considered the problem of finding a positive solution and multiple sign changing solutions to the problem with small energy, under symmetry assumptions on Ω and W, which allow finite symmetries, and some assumptions on the decay of W at infinity.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2013-11-01 and is currently open access. It has received 130 citations till now. The article focuses on the topics: Domain (ring theory).read more
Citations
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A guide to the Choquard equation
TL;DR: A survey of the existence and properties of solutions to the Choquard type equations can be found in this paper, where some variants and extensions of its variants can also be found.
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The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
Fashun Gao,Minbo Yang +1 more
TL;DR: In this paper, the Brezis-Nirenberg type problem of the nonlinear Choquard equation was studied and existence results for the problem were established for the case where Ω is a bounded domain of R with Lipschitz boundary.
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Nodal solutions for the Choquard equation
TL;DR: In this paper, the general Choquard equation is considered and minimal action odd solutions for p ∈ (N + α N, N + α n − 2 ) and minimal-action nodal solutions for n ∈ 2, N+α N − 2, N+ α N−2 ) are presented.
Journal ArticleDOI
A guide to the Choquard equation
TL;DR: A survey of the existence and properties of solutions to the Choquard type equations can be found in this article, where some variants and extensions of its variants can also be found.
Journal ArticleDOI
Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
TL;DR: In this article, the authors consider nonlinear Choquard equation where N ≥ 3, V ∈ L∞(ℝN) is an external potential and Iα(x) is the Riesz potential of order α ∈ (0, N).
References
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On Gravity's Role in Quantum State Reduction
Roger Penrose,Roger Penrose +1 more
TL;DR: In this paper, the stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity.
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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.
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The principle of symmetric criticality
TL;DR: In this article, it is shown that if a variational principle is invariant under some symmetry group G, then to test whether a symmetric field configuration ϕ is an extremal, it suffices to check the vanishing of the first variation of the action corresponding to variations ϕ + δϕ that are also symmetric.
On gravity's role in quantum state reduction
Roger Penrose,Roger Penrose +1 more
TL;DR: In this paper, the stability of a quantum superposition of two different stationary mass distributions is examined, where the perturbing effect of each distribution on the space-time structure is taken into account, in accordance with the principles of general relativity.
Journal ArticleDOI
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
TL;DR: In this paper, the authors considered a semilinear elliptic problem and proved the existence of a positive groundstate solution of the Choquard or nonlinear Schr\"odinger--Newton equation for an optimal range of parameters.