Normalized solutions for Schödinger equations with potential and general nonlinearities involving critical case on large convex domains

2023/11/03 by Jun Wang, Zhaoyang Yin, Wang, Jun +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2311.04914

Abstract

In this paper, we study the following Schrödinger equations with potentials and general nonlinearities \\beginaligned amp; -Δu+V(x)u+λu=|u|^q-2u+βf(u),
amp; ∫ |u|²dx=Θ, \endaligned . both on ℝ^N as well as on domains r Ω where Ω⊂ ℝ^N is an open bounded convex domain and r>0 is large. The exponent satisfies 2+(4)/(N)≤ q≤2^*=(2 N)/(N-2) and f:ℝ→ ℝ satisfies L²-subcritical or L²-critical growth. This paper generalizes the conclusion of Bartsch et al. in \citeTBAQ2023(2023, arXiv preprint). Moreover, we consider the Sobolev critical case and L²-critical case of the above problem.

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