Ground state solutions for modified quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

2020 ◽  
pp. 1-10
Author(s):  
Yingying Xiao ◽  
Chuanxi Zhu ◽  
Jianhua Chen
Keyword(s):  
Gauge Theory ◽  
Ground State ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Chern Simons

scholarly journals New results on the existence of ground state solutions for generalized quasilinear Schrödinger equations coupled with the Chern–Simons gauge theory

2021 ◽  
pp. 1-17
Author(s):  
Yingying Xiao ◽  
Chuanxi Zhu
Keyword(s):  
Gauge Theory ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions ◽  
Chern Simons ◽  
Constraint Minimization

In this paper, we study the following quasilinear Schrödinger equation − Δ u + V ( x ) u − κ u Δ ( u 2 ) + μ h 2 ( | x | ) | x | 2 ( 1 + κ u 2 ) u + μ ( ∫ | x | + ∞ h ( s ) s ( 2 + κ u 2 ( s ) ) u 2 ( s ) d s ) u = f ( u ) in   R 2 , κ > 0 V ∈ C 1 ( R 2 , R ) and f ∈ C ( R , R ) By using a constraint minimization of Pohožaev–Nehari type and analytic techniques, we obtain the existence of ground state solutions.

Standing waves of modified Schrödinger equations coupled with the Chern–Simons gauge theory

2019 ◽  
Vol 150 (4) ◽  
pp. 1915-1936 ◽  
Author(s):  
Pietro d'Avenia ◽  
Alessio Pomponio ◽  
Tatsuya Watanabe
Keyword(s):  
Gauge Theory ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Standing Waves ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Ground State Solutions ◽  
Chern Simons ◽  
Constraint Minimization

AbstractWe are interested in standing waves of a modified Schrödinger equation coupled with the Chern–Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the nonexistence for nontrivial solutions.

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