Acta Mathematicae Applicatae Sinica, English Series

, Volume 26, Issue 3, pp 387–394

Multiplicity of solutions for a class of Kirchhoff type problems


DOI: 10.1007/s10255-010-0005-2

Cite this article as:
He, Xm. & Zou, Wm. Acta Math. Appl. Sin. Engl. Ser. (2010) 26: 387. doi:10.1007/s10255-010-0005-2


In this paper we apply the (variant) fountain theorems to study the symmetric nonlinear Kirchhoff nonlocal problems. Under the Ambrosetti-Rabinowitz’s 4-superlinearity condition, or no Ambrosetti-Rabinowitz’s 4-superlinearity condition, we present two results of existence of infinitely many large energy solutions, respectively.


Kirchhoff nonlocal problemsMultiple solutionsFountain theorems

2000 MR Subject Classification


Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of ScienceMinzu University of ChinaBeijingChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina