ABSTRACT
In this paper, we consider a class of Kirchhoff problems as follows (1) (1) where a, b>0 are given constants, ϵ is a small parameter and . We first prove the nondegeneracy of positive solutions to Equation (1) when . Then, as an application, using a perturbed argument and finite-dimensional reduction method, we prove the existence of positive solutions of Equation (1) for ϵ small.
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Acknowledgments
The authors would like to thank Professor Shuangjie Peng very much for stimulating discussions and helpful suggestions on the present paper.
Disclosure statement
No potential conflict of interest was reported by the authors.