Multiple positive solutions for Kirchhoff type problems involving   concave and critical nonlinearities in ${R}^3$
  In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness principle we prove that the Kirchhoff problem has at least two solutions. 
Xiaofei Cao, Junxiang Xu and Jun Wang
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