Infinite Sharp Conditions by Nehari Manifolds for Nonlinear Schrödinger Equations

  • Wei Lian
  • Jihong Shen
  • Runzhang XuEmail author
  • Yanbing Yang


We study the Cauchy problem of nonlinear Schrödinger equation \(i\varphi _t+\Delta \varphi +|\varphi |^{p-1}\varphi =0\). By constructing infinite Nehari manifolds with geometric features, we not only obtain infinite invariant sets of solutions, but also give infinite sharp conditions for global existence and finite time blow up of solutions.


Nonlinear Schrödinger equation Potential wells Global existence Blow up Invariant set 

Mathematics Subject Classification

35Q55 35Q41 



This work was supported by the National Natural Science Foundation of China (11871017), the China Postdoctoral Science Foundation (2013M540270), and the Fundamental Research Funds for the Central Universities. Yang was supported by the National Natural Science Foundation of China (11801114).


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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  • Wei Lian
    • 1
  • Jihong Shen
    • 2
  • Runzhang Xu
    • 1
    • 2
    Email author
  • Yanbing Yang
    • 2
  1. 1.College of AutomationHarbin Engineering UniversityHarbinPeople’s Republic of China
  2. 2.College of Mathematical SciencesHarbin Engineering UniversityHarbinPeople’s Republic of China

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