ABSTRACT
In this paper, we are concerned with nodal solutions for a class of Kirchhoff-type problems where , a, b>0, f satisfies some asymptotically linear growth conditions. First of all, when N = 3, b>0 and , b>0 sufficiently small, we attain infinitely many nodal solutions by an equivalent transformation. Based on this, via a new and direct approach, the least energy sign-changing radial solutions can be obtained for the above problem. What's more, we also establish non-existence results of nodal solutions for and b large enough.
Acknowledgements
The author is grateful to Prof. David G. Costa for his helpful discussion and so many supports for her researches. The author also wishes to thank the anonymous referees for their valuable suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).