Webdiscussed above. This gives us a valid solution to the corresponding quadratic program. 3. If answer to X is NO, then answer to Y is NO; use contrapositive. If we have a solution …
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WebOct 16, 2024 · Abstract Standing waves solutions for a coupled Hartree–Fock type nonlocal elliptic system are considered. This nonlocal type problem was considered in … 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 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... WebJul 30, 2024 · Recently, Dai-Liu-Qin [28] classified nonnegative classical solutions to Schrödinger-Hartree-Maxwell type equation (1.5) in the full range s := m + α 2 ∈ (0, n 2 ), m ≥ 0 is an integer, 0 <...
Webclassification 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 … WebThis paper is concerned with the positive solutions of a class of static Hartree-type equations. We translate these equations to the equivalent integral systems involving the Riesz potentials. Using the regularity lifting lemma by contracting operators, we obtain the integrability result for the integrable solution u of integral systems.
WebApr 1, 2024 · Dai, Fang and Qin [25] classified all the positive classical solutions to (1.1) when c 2 = 0, a = 0, 0 < α < 2, σ = 2α ∈ (0, n), q 1 = 2 and p 1 = 1 via a direct method of moving planes for...
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* … it\u0027s for the boysWebSep 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 … it\u0027s for the image 意味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 assumptions, we approximate the solution in terms of a time dependent coherent state, whose phase and amplitude can be determined by a classical flow. it\\u0027s for the kidsWebOct 1, 2024 · Abstract 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∈RN,... it\u0027s for the greater good memeWebDec 1, 2024 · Classical solutions to a Hartree type system. This paper is concerned with positive classical solutions to the nonlocal system of Hartree type … it\u0027s for themWebThis 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*} … netally spectrum xtWebMar 1, 2012 · We study the asymptotic behavior of the Schr\"odinger equation in the presence of a nonlinearity of Hartree type in the semi-classical regime. Our scaling corresponds to a weakly nonlinear... it\u0027s forty below and i don\u0027t give a