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In this paper, we study the nonexistence and existence of normalized solutions for the nonlinear Kirchhoff-type equation −a+b∫RN|∇u|2dxΔu=λu+|u|p−2u+|u|q−2u 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.
Liu et al. (Mon,) studied this question.
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