NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions（λc,uc）∈R × H1（RN） to the general Kirchhoff problem ■ satisfying the normalization constraint■,where M ∈C（[0,∞）) is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44-75] and a direct correspondence,so we can handle in a unified way the nonlinearities g（s）,which are either mass subcritical,mass critical or mass supercritical.