Strongly interacting bumps for the Schrödinger–Newton equations

By Jun-cheng Wei, Matthias Winter. 2009

236 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ffb0c958c92f6276b7c85c6f24dcc45c20b2738c

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Citations in the corpus

Semi-classical states for the Choquard equation (2013, methodology): “In the case N = 3 , α = 2 , p = 2 , families of solutions for the Choquard equation which concentrate to nondegenerate critical points of V have been constructed in [50, 54] via a Lyapunov–Schmidt type reduction techniques.”
On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents (2016, background): “der the assumptions of Berestycki-Lions type; [3] for the existence of multibump shaped solution for the equation with deepening potential well; [23, 30] for the existence of sign-changing solutions; [4, 5, 40, 47] for the existence and concentration behavior of the semiclassical solutions. To the b”
Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth (2018, unknown): “In [60],Wei andWinter considered thenonlocal equation, equivalent to the Schrödinger–Newton system, − ε2∆v + V(x)v = ε(I2 ∗ v2)v, x ∈ R3, (1.”
Positive and sign changing solutions to a nonlinear Choquard equation (2012, background): “Further results for related problems may be found in [1, 7, 8, 18, 22, 25, 26] and the references therein.”
Multi-bump solutions for Choquard equation with deepening potential well (2015, background): “d an approach to prove the existence of inﬁnitely many geometrically distinct weak solutions. For other related results, we refer the readers to [11, 18] for the existence of sign-changing solutions, [27, 32, 35] for the existence and concentration behavior of the semiclassical solutions and [28] fo”
Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations (2020, background): “For the Choquard-type equation and related problems, we refer to [11,31,33,44] for the existence of solutions and multiplicity properties, to [13,22,47] for existence of sign-changing solutions, and to [12,32,45,48] for semiclassical solutions.”
The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation (2016, background): “For other related results, we refer the readers to [14, 17] for the existence of sign-changing solutions, [4, 5, 27, 32, 36, 39] for the existence and concentration behavior of the semiclassical solutions.”
Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains (2012, background): “Winter [39] have considered the singular perturbation problem (1.”
Existence and concentration of ground state solutions for a critical nonlocal Schr\"odinger equation in $\R^2$ (2016, methodology): “d for the critical equation in the sense of Hardy-Littlewood-Sobolev inequality. For N = 3, µ = 1 and F(s) = 1 2|s|2, by proving the uniqueness and non-degeneracy of the ground states, Wei and Winter [47] constructed a family of solutions by a Lyapunov-Schmidt type 2 reduction when inf V > 0. In ”
Singularly perturbed critical Choquard equations (2016, background): “For N = 3, μ = 1 and F (s) = |s|2, the uniqueness and non-degeneracy of the ground states were proved in Lenzmann, Wei and Winter in [21, 33].”
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics (2012, background): “ E.H.Lieb has proved that the groundstate uis radial and unique up to translations [16]. Wei Juncheng and M.Winter have shown that the groundstate is up to translations a nondegenerate critical point [32]. The symmetry and the regularity of solutions have been proved under the assumption p≥ 2 and [2”