In this paper, we study the multiplicity of solutions with a prescribed 54989" 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 4d328e45401ae0c07e2e9" title="Click to view the MathML source">a,b>0 are constants, λ∈R, 5466f94a6d05eb3b">. To get such solutions we look for critical points of the energy functional
For the value 5466f94a6d05eb3b"> considered, the functional Ib is unbounded from below on Sr(c). By using a minimax procedure, we prove that for any 548ef44eb8a13c8b834e15e82f42b5e" title="Click to view the MathML source">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+.