In this paper, we study the multiplicity of solutions with a prescribed S1468121816300426&_mathId=si2.gif&_user=111111111&_pii=S1468121816300426&_rdoc=1&_issn=14681218&md5=1caf88f83c5880c73b6bc703f9054989" title="Click to view the MathML source">L2-norm for a class of nonlinear Kirchhoff type problems in R3
−(a+b∫R3|∇u|2)Δu−λu=|u|p−2u,
where a,b>0 are constants, λ∈R, . To get such solutions we look for critical points of the energy functional
restricted on the following set
For the value considered, the functional Ib is unbounded from below on Sr(c). By using a minimax procedure, we prove that for any c>0, there are infinitely many critical points of Ib restricted on Sr(c) with the energy . Moreover, we regard b as a parameter and give a convergence property of as b→0+.