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Abstract
We reprove a result by Bartsch, Weth, and Willem (Calc. Var. Partial Differ. Equ. 18(3):253–268, 2003) concerning the nondegeneracy of bubble solutions for a critical semilinear elliptic equation involving the polyharmonic operator. The merit of our proof is that it does not rely on the comparison theorem. The argument of our proof mainly uses the stereographic projection with the Funk–Hecke formula, which works for general critical semilinear elliptic equations.
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Details
1 Guangxi University, Nanning, China (GRID:grid.256609.e) (ISNI:0000 0001 2254 5798)
2 Nanjing Forestry University, College of Science, Nanjing, China (GRID:grid.410625.4) (ISNI:0000 0001 2293 4910)
3 Nanjing University of Information Science and Technology, School of Mathematics and Statistics, Nanjing, China (GRID:grid.260478.f) (ISNI:0000 0000 9249 2313)