A perturbed Kirchhoff problem with critical exponent

摘要

In this paper, we consider a class of Kirchhoff problems as follows @@@ - (a + b integral(RN)vertical bar del u vertical bar(2)) Delta u = (1 + epsilon K(x))u(2*-1), u > 0 in R-N, (1) @@@ where a, b > 0 are given constants, epsilon is a small parameter and 2* = 2N/(N - 2), N >= 3. We first prove the nondegeneracy of positive solutions to Equation (1) when epsilon = 0. Then, as an application, using a perturbed argument and finite-dimensional reduction method, we prove the existence of positive solutions of Equation (1) for epsilon small.

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