A global branch approach to normalized solutions for the Schrödinger equation

2021/12/10 by Jeanjean, Louis, Zhang, Jianjun, Zhong, Xuexiu · 2 citations
#35A02 #35A16 #35B40 #35J60 #46N50 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.05869

Abstract

We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form -Δu+λu=g(u), u ∈ H¹(ℝ^N), N ≥ 1. Our approach permits to handle in a unified way nonlinearities g(s) which are either mass subcritical, mass critical or mass supercritical. Among its main ingredients is the study of the asymptotic behaviors of the positive solutions as λ→ 0⁺ or λ→ +∞ and the existence of an unbounded continuum of solutions in (0, + ∞) × H¹(ℝ^N).

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• Normalized solutions of L² supercritical NLS equations in exterior domains with inhomogeneous nonlinearities
• Normalized Solutions for the (2,q)-Laplacian Operator Between Mass-Critical Exponents

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