Normalized Ground State Solutions of Nonlinear Schrödinger Equations Involving Exponential Critical Growth

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...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of geometric analysis 2023-03, Vol.33 (3), Article 83
Main Authors: Chang, Xiaojun, Liu, Manting, Yan, Duokui
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Ground state
Lagrange multiplier
Mathematics
Mathematics and Statistics
Schrodinger equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 .
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01130-8