In this paper, we study the multiplicity of solutions with a prescribed 88f83c5880c73b6bc703f9054989" 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 e9904d328e45401ae0c07e2e9" title="Click to view the MathML source">a,b>0 are constants, λ∈R, . To get such solutions we look for critical points of the energy functional
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 99107f8ff5e837cb62a1196"> of Ib restricted on Sr(c) with the energy 999291cb723ef0d16f1aa199f86b">. Moreover, we regard 99f75351cdd4351ecae1c9008" title="Click to view the MathML source">b as a parameter and give a convergence property of as bed5cbdc052e06" title="Click to view the MathML source">b→0+.