147,510 research outputs found
Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System
A relatively complete picture on the steady states of the following
Schrdinger-Poisson-Slater (SPS) system \begin{cases} -\Delta
Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as
}x\to\infty,\\ -\Delta V=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 &
\mbox{as }x\to\infty. \end{cases}
is given in this paper: existence, uniqueness, regularity and asymptotic
behavior at infinity, where is a constant. To the author's knowledge,
this is the first uniqueness result on SPS system
Quantum Dilaton Gravity in the Light-cone Gauge
Recently, models of two-dimensional dilaton gravity have been shown to admit
classical black-hole solutions that exhibit Hawking radiation at the
semi-classical level. These classical and semi-classical analyses have been
performed in conformal gauge. We show in this paper that a similar analysis in
the light--cone gauge leads to the same results. Moreover, quantization of
matter fields in light--cone gauge can be naturally extended to include
quantizing the metric field {\it \`a la} KPZ. We argue that this may provide a
new framework to address many issues associated to black-hole physics.Comment: 16 pages, Use phyzzx, CERN-TH.6633/9
Inverse Jacobian multipliers and Hopf bifurcation on center manifolds
In this paper we consider a class of higher dimensional differential systems
in which have a two dimensional center manifold at the origin
with a pair of pure imaginary eigenvalues. First we characterize the existence
of either analytic or inverse Jacobian multipliers of the systems
around the origin, which is either a center or a focus on the center manifold.
Later we study the cyclicity of the system at the origin through Hopf
bifurcation by using the vanishing multiplicity of the inverse Jacobian
multiplier.Comment: 22. Journal of Differential Equation, 201
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