45,338 research outputs found
Existence of stable solutions to in with and
We consider the polyharmonic equation in
with and . We prove the existence of many entire stable
solutions. This answer some questions raised by Farina and Ferrero
Geometric characterization on the solvability of regulator equations
The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The ‘feedback’ part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained
Location of Poles for the Hastings-McLeod Solution to the Second Painlev\'{e} Equation
We show that the well-known Hastings-McLeod solution to the second
Painlev\'{e} equation is pole-free in the region , which
proves an important special case of a general conjecture concerning pole
distributions of Painlev\'{e} transcedents proposed by Novokshenov. Our
strategy is to construct explicit quasi-solutions approximating the
Hastings-McLeod solution in different regions of the complex plane, and
estimate the errors rigorously. The main idea is very similar to the one used
to prove Dubrovin's conjecture for the first Painlev\'{e} equation, but there
are various technical improvements.Comment: 31 pages, 2 figures. Minor revision, to appear in Constructive
Approximatio
Minkowski Brane in Asymptotic dS Spacetime without Fine-tuning
We discuss properties of a 3-brane in an asymptotic 5-dimensional de-Sitter
spacetime. It is found that a Minkowski solution can be obtained without
fine-tuning. In the model, the tiny observed positive cosmological constant is
interpreted as a curvature of 5-dimensional manifold, but the Minkowski
spacetime, where we live, is a natural 3-brane perpendicular to the fifth
coordinate axis.Comment: 6 pages, Latex fil
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