Blowup analysis for a nonlinear equation with negative exponent (Q2634157)

The paper is concerned with the blowup behavior of the minimizing sequence to the nonlinear equation with negative critical exponents \[ 4 u_{\theta\theta}+u=R(\theta) u^{p-1},\,\,\, u>0, \text{ on } \mathbb{S}^1, \] where \(p=-2\) or \(p=\varepsilon-2\) with \(\varepsilon\in (0,2)\), and \(R(\theta)\) is a \(C^1(\mathbb{S}^1)\) and positive function. The authors investigate the location for blowup point and the asymptotic behavior of solutions near the blowup point.