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Abstract
We consider a class of indefinite Kirchhoff-type equations:
where ,
,
and
. We require that f(x, u) is “local" sublinear at the origin and “local" linear at infinity on u, respectively. Using mountain pass theorem and Ekeland variational principle, we obtain the existence and multiplicity of nontrivial solutions. In particular, the existence criterion of three nontrivial solutions is established. Furthermore, the nonexistence of nontrivial solutions is explored as well.
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Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
J. Sun was supported by the National Natural Science Foundation of China [grant number 11201270], [grant number 11271372]; Shandong Province Natural Science Foundation [grant number ZR2012AQ010], [grant number ZR2015JL002]; China Postdoctoral Science Foundation [grant number 2014M551494], [grant number 2015T80491] and Young Teacher Support Program of Shandong University of Technology. T.-F. Wu was supported in part by the Ministry of Science and Technology and the National Center for Theoretical Sciences, Taiwan.