On somep-Laplacian equation with electromagnetic fields and critical nonlinearity in ℝN

2015 ◽  
Vol 56 (4) ◽  
pp. 041504 ◽  
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Electromagnetic Fields ◽  
Critical Nonlinearity ◽  
Laplacian Equation

Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity

2010 ◽  
Vol 54 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Standing Wave ◽  
Electromagnetic Fields ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Critical Nonlinearity ◽  
Existence And Multiplicity ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Image Position

AbstractWe consider the existence and multiplicity of standing-wave solutionsof nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearityUnder suitable assumptions, we prove that it has at least one solution and that, for any m ∈ ℕ, it has at least m pairs of solutions.

scholarly journals Existence of Nontrivial Solutions for Perturbedp-Laplacian Equation inℝNwith Critical Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Huixing Zhang ◽  
Xiaoqian Liu
Keyword(s):  
Variational Method ◽  
Positive Solution ◽  
Critical Nonlinearity ◽  
Nontrivial Solutions ◽  
Laplacian Equation

We consider a perturbedp-Laplacian equation with critical nonlinearity inℝN. By using variational method, we show that it has at least one positive solution under the proper conditions.

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