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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2024

A global branch approach to normalized solutions for the Schrödinger equation

Résumé

We present a novel approach to study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schr\"odinger equation of the form \begin{equation*} -\Delta u+\lambda u=g(u), \quad u \in H^1(\mathbb{R}^N), \, N \geq 1. \end{equation*} This 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 $\lambda\rightarrow 0^+$ or $\lambda\rightarrow +\infty$ and the existence of an unbounded continuum of solutions in $(0, + \infty) \times H^1(\mathbb{R}^N)$

Dates et versions

hal-03489486 , version 1 (17-12-2021)

Identifiants

Citer

Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong. A global branch approach to normalized solutions for the Schrödinger equation. Journal de Mathématiques Pures et Appliquées, 2024, 183, pp.44-75. ⟨10.1016/j.matpur.2024.01.004⟩. ⟨hal-03489486⟩
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