Normalized solutions to Schödinger equations with potential and inhomogeneous nonlinearities on large convex domains

2023/06/13 by Bartsch, Thomas, Qi, Shijie, Zou, Wenming
#35A01) #35J60 (35B09 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07826

Abstract

The paper addresses an open problem raised in [Bartsch, Molle, Rizzi, Verzini: Normalized solutions of mass supercritical Schrödinger equations with potential, Comm. Part. Diff. Equ. 46 (2021), 1729-1756] on the existence of normalized solutions to Schrödinger equations with potentials and inhomogeneous nonlinearities. We consider the problem -Δu+V(x)u+λu = |u|^q-2u+β|u|^p-2u, ‖u‖²₂=∫|u|²dx = α, both on ℝ^N as well as on domains rΩ where Ω⊂ℝ^N is an open bounded convex domain and r>0 is large. The exponents satisfy 2

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