scholarly journals Infinitely Many Standing Waves for the Nonlinear Chern-Simons-Schrödinger Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Jinmyoung Seok
Keyword(s):  
Wide Class ◽  
Standing Waves ◽  
Schrodinger Equations ◽  
Infinitely Many Solutions ◽  
Schrödinger Equations ◽  
Power Type ◽  
Chern Simons

We prove the existence of infinitely many solutions of the nonlinear Chern-Simons-Schrödinger equations under a wide class of nonlinearities. This class includes the standard power-type nonlinearity with exponentp>4. This extends the previous result which covers the exponentp>6.

scholarly journals Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Na Zhang ◽  
Jie Xin
Keyword(s):  
Minimization Problem ◽  
Standing Waves ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Power Type ◽  
Initial Value ◽  
Fractional Schrödinger Equations ◽  
Nonlinear Fractional Schrödinger Equations ◽  
Existence And Stability ◽  
Constrained Minimization Problem

We consider the standing wave solutions for nonlinear fractional Schrödinger equations with focusing Hartree type and power type nonlinearities. We first establish the constrained minimization problem via applying variational method. Under certain conditions, we then show the existence of standing waves. Finally, we prove that the set of minimizers for the initial value problem of this minimization problem is stable.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

Infinitely many solutions for cubic nonlinear Schrödinger equations in dimension four

2017 ◽  
Vol 8 (1) ◽  
pp. 715-724 ◽  
Author(s):  
Jérôme Vétois ◽  
Shaodong Wang
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Infinitely Many Solutions ◽  
Schrödinger Equations ◽  
Optimal Dimension ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

Abstract We extend Chen, Wei and Yan’s constructions of families of solutions with unbounded energies [5] to the case of cubic nonlinear Schrödinger equations in the optimal dimension four.

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