/pdf/liouville-type-theorems-and-harnack-type-inequalities-for-5d4tzr6rso.pdf

Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations

Infinitely many solutions for the prescribed scalar curvature problem on SN

On the prescribed scalar curvature problem in RN, local uniqueness and periodicity

A direct method of moving spheres on fractional order equations

In this paper we prove some existence results concerning a problem arising in conformal differential geometry. Consider a smooth metric g onB = {x ∈ R : |x| < 1}, the unit ball onR, n ≥ 3, and let∆g, Rg, νg, hg denote, respectively, the Laplace-Beltrami operator, the scalar curvature of (B, g), the outward unit normal to∂B = Sn−1 with respect tog and the mean curvature of (Sn−1, g). Given two smooth functions R′ andh′, we will be concerned with the existence of positive solutionsu ∈ H 1(B) of   −4(n− 1) (n− 2)∆gu+ Rgu = R ′u n+2 n−2 , in B;

/pdf/on-the-yamabe-problem-and-the-scalar-curvature-problems-3gy6ivsox6.pdf

On the Yamabe problem and the scalar curvature problems under boundary conditions

on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a negative answer. We showed that a necessary condition for (1) to have a solution is: R′(r) changes signs in the region where R is positive. (2)

/pdf/prescribing-scalar-curvature-on-sn-qw4i9zqzbs.pdf

Congming Li

Papers

Prescribing scalar curvature on Sn