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- Title
Normalized Ground State Solutions of Nonlinear Schrödinger Equations Involving Exponential Critical Growth.
- Authors
Chang, Xiaojun; Liu, Manting; Yan, Duokui
- Abstract
We are concerned with the following nonlinear Schrödinger equation: - Δ u + λ u = f (u) in R 2 , u ∈ H 1 (R 2) , ∫ R 2 u 2 d x = ρ , where ρ > 0 is given, λ ∈ R arises as a Lagrange multiplier and f satisfies an exponential critical growth. Without assuming the Ambrosetti–Rabinowitz condition, we show the existence of normalized ground state solutions for any ρ > 0 . The proof is based on a constrained minimization method and the Trudinger–Moser inequality in R 2 .
- Subjects
WAVE mechanics; PARTIAL differential equations; EXPONENTIAL functions; MATHEMATICS; SCHRODINGER equation
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 3, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-022-01130-8