In this paper, we study the multiplicity of solutions with a prescribed 5880c73b6bc703f9054989" 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 8e45401ae0c07e2e9" title="Click to view the MathML source">a,b>0 are constants, 8e320c52d429d6cc" title="Click to view the MathML source">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 8ef44eb8a13c8b834e15e82f42b5e" 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+.