Structure of Singular Solutions for Nonlinear Elliptic Equations with the Critical Potential
陳志和先生國立中央大學數學系 上午 10:00–10:50 鴻經館 107 室Abstract：
We consider the structure of singular solutions for elliptic equations with the Hardy potential and critical nonlinearity under quite general conditions on the potential terms. It is shown that there exists a unique special singular solution, and other infinitely many singular solutions are oscillatory around the special singular solution. We also study the asymptotic behavior of the solutions around the singular point. Our results can be applied to various problems such as the scalar feld equation, a self-replication model and the Cafarelli-Kohn-Nirenberg inequality.