二阶非线性薛定谔方程解的门槛条件研究
Study on the Threshold Conditions for Solutions of the Second-Order Nonlinear Schrodinger Equation
摘要: 本文研究了定义在R^（N>3)上的二阶非线性薛定谔方程，其非线性指数介于质量临界与能量次 临界之间。通过构造Pohozaev-Nehari不变流形，在位势井理论框架下，得到了解整体存在与有 限时间爆破的门槛条件。
Abstract: This paper investigates the second-order nonlinear Schrodinger equation defined on , with the nonlinear exponent lying between the mass-critical and energysubcritical regimes. By constructing Pohozaev-Nehari cross-invariant manifolds, we establish sharp thresholds for global existence and finite-time blow-up within the potential well framework.
文章引用：孔鑫宇, 林强. 二阶非线性薛定谔方程解的门槛条件研究[J]. 理论数学, 2026, 16(6): 48-61. https://doi.org/10.12677/PM.2026.166156

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