Non-degeneracy of least-energy solutions for an elliptic problem with nearly critical nonlinearity

作者：Takahashi Futoshi^*

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2010, 140: 203-222.

DOI：10.1017/S0308210509000419

We consider the problem -Delta u = c(0)K (x)u(p epsilon); u > 0 in Omega, v = 0 on partial derivative Omega, where Omega is a smooth, bounded domain in R(N), N >= 3; c(0) = N(N - 2), p(epsilon) = (N + 2)/(N - 2) - epsilon and K is a smooth, positive function on (Omega) over bar. We prove that least-energy solutions of the above problem are non-degenerate for small epsilon > 0 under some assumptions on the coefficient function K. This is a generalization of the recent result by Grossi for K = 1, and needs precise estimates and a new argument.

• 出版日期2010