Journal ArticleDOI
On the structure of the conformal Gaussian curvature equation on ℝ2
Kuo Shung Cheng,Wei Ming Ni +1 more
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This article is published in Duke Mathematical Journal.The article was published on 1991-04-01. It has received 49 citations till now. The article focuses on the topics: Scalar curvature & Mean curvature.read more
Citations
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Journal ArticleDOI
Radial Symmetry of Positive Solutions of Nonlinear Elliptic Equations in Rn
Yi Li,Wei Ming Ni +1 more
TL;DR: In this paper, Radial symmetry of positive solutions of nonlinear elliptic equations in Rn is studied. But the authors focus on the nonlinear version of the problem and do not consider the non-linear version.
Journal ArticleDOI
Qualitative properties of solutions to some nonlinear elliptic equations in r 2
Wenxiong Chen,Congming Li +1 more
TL;DR: In this article, the authors investigated properties of the solutions to the -Au R(x)e u(x), x R 2 R 2 for functions R (x) which are positive near infinity and proved that all the solutions satisfy an identity.
Book ChapterDOI
CHAPTER 3 - Qualitative Properties of Solutions to Elliptic Problems
TL;DR: In this paper, a survey of qualitative properties of elliptic solutions to elliptic equations is presented, focusing on two properties of solutions: the shape of solutions and the stability of solutions.
Journal ArticleDOI
Pattern formations in two-dimensional Gray-Scott model: existence of single-spot solutions and their stability
TL;DR: In this paper, the stability and instability of the 2D Gray-Scott model were established in terms of the parameters involved in two single-spot solutions, and the stability of these solutions was analyzed.
References
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Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book
Topics in stability and bifurcation theory
TL;DR: In this paper, the mathematical problems of hydrodynamic stability and topological degree theory and applications are discussed. But the real world is not considered. And there is no solution to the nonlinear elliptic boundary value problems of second order.
Journal ArticleDOI
An extension of Schwarz’s lemma
TL;DR: In this paper, the authors define a Riemann surface as an analytic function o = f(z) from the circle I zx < 1 to a riemannian surface W. The analyticity is expressed by the fact that every local parameter w is a function of z. The corresponding value of ds =X j dw|N dz I is therefore uniquely de* Presented to the Society, September 8, 1937; received by the editors April 1, 1937.