Asymptotic non-degeneracy of multiple blowup solutions to the Liouville-Gel%26apos;fand problem with an inhomogeneous coefficient

作者：Ohtsuka Hiroshi; Sato Tomohiko^*; Suzuki Takashi

来源：Journal of Mathematical Analysis and Applications, 2013, 398(2): 692-706.

DOI：10.1016/j.jmaa.2012.09.028

• Blowup analysis
• Non-degeneracy
• Green%26apos
• s function
• The Hamiltonian

We study asymptotic non-degeneracy of multi-point blowup solutions to the Liouville-Gel%26apos;fand problem -Delta u = lambda ye(u) in a two-dimensional bounded smooth domain with a Dirichlet boundary condition. Here lambda %26gt; 0 is a parameter and V is a positive C-1 function on (Omega) over bar. It is known that the solution concentrates on a critical point of a Hamiltonian as lambda down arrow 0. We show that if this critical point is non-degenerate, then the associated solution is linearly non-degenerate, which is a natural extension of the case V 1. Technical modifications are used in the proof to control residual terms.

• 出版日期2013-2-15