Classical solutions to a hartree type system
WebJun 1, 2011 · In this paper we consider the nonlinear Hartree equation in presence of a given external potential, for an initial coherent state. Under suitable smoothness … WebJun 19, 2024 · The aim of this paper is to prove the nondegeneracy of the unique positive solutions for the following critical Hartree type equations when μ>0 is close to 0, −Δu=Iμ∗u2μ∗u2μ∗−1,x∈ ...
Classical solutions to a hartree type system
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WebApr 7, 2024 · We prove that, for a smooth two-body potentials, the quantum mean-field approximation to the nonlinear Schroedinger equation of the Hartree type is stable at the classical limit h \to 0, yielding ... WebThis paper is concerned with positive classical solutions to the nonlocal system of Hartree type −Δu=1 x n−α∗vpvp−1inRn,−Δv=1 x n−β∗uquq−1inRn,\begin{equation*} …
WebMay 15, 2024 · Abstract This paper is concerned with positive classical solutions to the Hartree equation ⁎ − Δ u = ( 1 x n − α ⁎ u p) u p − 1 in R n. When n ≤ 2, we show that …
WebThis paper is concerned with positive classical solutions to the nonlocal system of Hartree type −Δu=1 x n−α∗vpvp−1inRn,−Δv=1 x n−β∗uquq−1inRn,\begin {equation*} \def\eqcellsep {&}\begin {array} {rcl} \hspace* {85pt}-\Delta u &=& \displaystyle {\left (\frac {1} { x ^ {n-\alpha }} * v^p\right)} v^ {p-1} \quad \text { in }\mathbb {R}^n, \hspace* … WebMar 1, 2024 · This paper is concerned with positive classical solutions to the nonlocal system of Hartree type − Δ u = 1 x n − α ∗ v p v p − 1 in R n , − Δ v = 1 x n − β ∗ u q u q − ...
Webthe notion of the phase trajectory of a classical system. A mathematical framework for this approach was developed in [18]. For the Hartree-type equation, it proves to be ... the solutions to the Hartree-type equation are to be considered as essentially quantum. Obviously, Ψ(x,t,~) 2 is to tend to δ(x− X(t)) ...
WebDec 1, 2024 · Classical solutions to a Hartree type system. This paper is concerned with positive classical solutions to the nonlocal system of Hartree type … bridge military exerciseWebDec 27, 2024 · Dai, Fang, and Qin [23] classified all the positive classical solutions to (1.1) when m = 0, 0 < α < 2, σ = 2α ∈ (0, n), p = 2, and q = 1 via a direct method of moving planes for fractional... bridge mill apartment homes 30253WebSep 1, 2024 · In this paper, we are mainly concerned with the physically interesting static Schrodinger-Hartree-Maxwell type equations \begin {equation*} (-\Delta)^ {s}u (x)=\left (\frac {1} { x ^ {\sigma}}\ast u ^ {p}\right)u^ {q} (x) \,\,\,\,\,\,\,\,\,\,\,\, \text {in} \,\,\, \mathbb {R}^ {n} \end {equation*} involving higher-order or higher-order … bridge milk for exclusive breastfeedingWebNov 10, 2014 · where N ≥ 3, V ∈ L ∞ (ℝ N) is an external potential and I α (x) is the Riesz potential of order α ∈ (0, N). The power in the nonlocal part of the equation is critical with respect to the Hardy–Littlewood–Sobolev inequality. As a consequence, in the associated minimization problem a loss of compactness may occur. We prove that if then the … can\u0027t light pilot lightWebclassification of the nonnegative solutions to the system (0.1) by using the method of moving spheres. Finally, we prove Liouville-type theorems results for system (0.1) in the … can\u0027t lift shoulder laterallyWebOct 16, 2024 · Abstract Standing waves solutions for a coupled Hartree–Fock type nonlocal elliptic system are considered. This nonlocal type problem was considered in … bridgemill apartmentsWebSemantic Scholar extracted view of "Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system" by Kun Wang et al. Skip to search ... @article{Wang2024SymmetryOP, title={Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system}, author={Kun Wang and Minbo Yang}, journal={Appl. … bridgemill citizens assembly