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- Title
Normalized Solutions for Nonautonomous Schrödinger Equations on a Suitable Manifold.
- Authors
Chen, Sitong; Tang, Xianhua
- Abstract
In this paper, we prove the existence of normalized ground state solutions for the following Schrödinger equation - Δ u - a (x) f (u) = λ u , x ∈ R N ; u ∈ H 1 (R N) , and give a better representation of its geometrical structure, where N ≥ 1 , λ ∈ R , a ∈ C (R N , 0 , ∞)) with 0 < a ∞ : = lim | y | → ∞ a (y) ≤ a (x) and f ∈ C (R , R) satisfies general assumptions. In particular, we propose a new approach to recover the compactness for a minimizing sequence on a suitable manifold, and overcome the essential difficulties due to the nonconstant potential a.
- Publication
Journal of Geometric Analysis, 2020, Vol 30, Issue 2, p1637
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-019-00274-4