Nondegeneracy of solutions to the critical p$p$‐Laplace Kirchhoff equation

Abstract

We establish the nondegeneracy of solutions in suitable space to the following ‐Laplace Kirchhoff equation with critical Sobolev exponent: where , , and is the critical Sobolev exponent. In particular, we prove that uniqueness breaks down for high dimension , that is, we show that there exist two nondegenerate solutions that seem to be completely different from the result of critical ‐Laplace equation () or the low‐dimensional Kirchhoff equation (the case ).