TITLE:
A Note on Global Existence, Blow-Up and Orbital Stability of Standing Waves for the Schrödinger Equation with Mixed Nonlinearities
AUTHORS:
Hui Jian, Silin Xiao, Meixia Cai
KEYWORDS:
Nonlinear Schrödinger Equation, Mixed Nonlinearities, Blow-Up, Global Existence, Orbital Stability of Standing Waves
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.8,
August
25,
2025
ABSTRACT: This study is devoted to the global existence, blow-up and orbital stability of standing waves for the Schrödinger equation with mixed nonlinearities. Firstly, we derive some criteria for global existence and blow-up of the solutions by making use of the ground state and scaling techniques. Secondly, by taking advantage of the refined compactness argument, scaling techniques and the variational characterization of ground state solutions, we explore the
L
2
-concentration phenomenon and limiting behavior of blow-up solutions in the
L
2
-critical case with
μ=±1
and
1