Two solutions to Kazdan-Warner’s problem on surfaces
نویسندگان
چکیده
In this paper, we study the sign-changing Kazdan-Warnerâs problem on two dimensional closed Riemannian manifold with negative Euler number $\chi (M)<0$. We show that once direct method convex sets is used to find a minimizer of corresponding functional, then there another solution via use variational mountain pass. conclusion, are at least solutions Kazdan-Warner equation provided prescribed function changes signs and average.
منابع مشابه
Isothermic and S-Willmore Surfaces as Solutions to Blaschke’s Problem
Note that Blaschke and his school only considered surfaces in 3-space and ignored the higher co-dimension case. In Sn this problem is still meaningful. It is known that the construction of Darboux pair of isothermic surfaces as well as dual Willmore surfaces has a generalization to Sn (see [4, 9] and [7]), and they still constitute solutions to the generalized Blaschke’s problem. Here we will s...
متن کاملKazdan-Warner equation on graph
Let G = (V, E) be a connected finite graph and ∆ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such that the Kazdan-Warner equation ∆u = c− heu has a solution on V , where c is a constant, and h : V → R is a function. We also consider similar equations involving higher order derivatives on graph. Our results ...
متن کاملTwo solutions to the adaptive visual servoing problem
In this paper, we present two globally convergent vision-based position controllers for a planar two-links manipulator in the so-called fixed-camera configuration, where the camera orientation and scale factor are considered unknown. This is a basic adaptive visual servoing problem whose solution was hampered by the nonlinear dependence of the system dynamics on the unknown parameters. The cont...
متن کاملOn Solutions to a Seating Problem
The seating problem, proposed by Wu [2], deals with the following assignment of n couples in a row: n couples are seated in one row. Each person, except two seated at the two ends, has two neighbors. It is required that each neighbor of person k should either have the same gender or be the spouse of k. In this paper, we consider several solutions to the problem, both direct and indirect. Simula...
متن کاملOn “Solutions” to the Ecological Inference Problem
In his 1997 book, King announced “A Solution to the Ecological Inference Problem”. This review discusses King’s method, and tests it on data where truth is known. In the test data, his method produces results that are far from truth, and diagnostics are unreliable. Ecological regression makes estimates that are similar to King’s, while the neighborhood model is more accurate. His announcement i...
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: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15711