In this paper, we study the nonexistence and existence of normalized solutions for the nonlinear Kirchhoff-type equation a+bRN|u|2dxΔu=λu+|u|p2u+|u|q2u in RN with prescribed L2-norm, where N = 1, 2, 3, a, b > 0 are constants, q=2+8N is L2-critical exponent to Kirchhoff-type Equation, and p=2+4N is the L2-critical exponent to the “local” equation.

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