Multiplicity of Normalized Solutions for Sobolev Supercritical Schrödinger Equations With Potential

ABSTRACT In the present paper, we investigate the multiplicity of normalized solutions to the following Sobolev supercritical Schrödinger equation with potential where , , , , is an unknown parameter which will appear as a Lagrange multiplier, is a mass subcritical and Sobolev subcritical nonlinearity. Under fairly general assumptions about and a global condition about , with the aid of the cutoff technique and Moser iteration, we obtain the multiplicity of normalized solutions about the above equation. Our main contribution is related to the fact that we are able to deal with the case .