We investigate the existence of solutions to the fractional nonlinear Schrödinger equation (−Δ)su=f(u)−μu with prescribed L2-norm ∫Rjavax.xml.bind.JAXBElement@446caed1|u|2dx=m in the Sobolev space Hs(RN). Under fairly general assumptions on the nonlinearity f, we prove the existence of a ground state solution and a multiplicity result in the radially symmetric case.
Appolloni, L., Secchi, S. (2021). Normalized solutions for the fractional NLS with mass supercritical nonlinearity. JOURNAL OF DIFFERENTIAL EQUATIONS, 286, 248-283 [10.1016/j.jde.2021.03.016].
Normalized solutions for the fractional NLS with mass supercritical nonlinearity
Appolloni L.;Secchi S.
2021
Abstract
We investigate the existence of solutions to the fractional nonlinear Schrödinger equation (−Δ)su=f(u)−μu with prescribed L2-norm ∫Rjavax.xml.bind.JAXBElement@446caed1|u|2dx=m in the Sobolev space Hs(RN). Under fairly general assumptions on the nonlinearity f, we prove the existence of a ground state solution and a multiplicity result in the radially symmetric case.
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