Hilbert's 16th problem for classical Liénard equations of even degree
نویسندگان
چکیده
منابع مشابه
A Resolution to Hilberts First Problem
The continuum hypothesis (CH) is one of and if not the most important open problems in set theory, one that is important for both mathematical and philosophical reasons. The general problem is determining whether there is an infinite set of real numbers that cannot be put into one-to-one correspondence with the natural numbers or be put into one-to-one correspondence with the real numbers respe...
متن کاملDegree Ramsey numbers for even cycles
Let H s − → G denote that any s-coloring of E(H) contains a monochromatic G. The degree Ramsey number of a graph G, denoted by R∆(G, s), is min{∆(H) : H s − → G}. We consider degree Ramsey numbers where G is a fixed even cycle. Kinnersley, Milans, and West showed that R∆(C2k, s) ≥ 2s, and Kang and Perarnau showed that R∆(C4, s) = Θ(s 2). Our main result is that R∆(C6, s) = Θ(s 3/2) and R∆(C10, ...
متن کاملQuantitative Theory of Ordinary Differential Equations and Tangential Hilbert 16th Problem
These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...
متن کاملClassical Center Location Problem Under Uncertain Environment
This paper investigates the $p$-center location problem on a network in which vertex weights and distances between vertices are uncertain. The concepts of the $alpha$-$p$-center and the expected $p$-center are introduced. It is shown that the $alpha$-$p$-center and the expected $p$-center models can be transformed into corresponding deterministic models. Finally, linear time algorithms for find...
متن کاملTANGENTIAL VERSION OF HILBERT 16th PROBLEM FOR THE ABEL EQUATION
Two classical problems on plane polynomial vector fields, Hilbert’s 16th problem about the maximal number of limit cycles in such a system and Poincaré’s center-focus problem about conditions for all trajectories around a critical point to be closed, can be naturally reformulated for the Abel differential equation y′ = p(x)y + q(x)y. Recently, the center conditions for the Abel equation have be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2008
ISSN: 0022-0396
DOI: 10.1016/j.jde.2007.11.011