Existence and multiplicity results for anisotropic stationary Schrödinger equations

2014 ◽  
Vol 25 (1) ◽  
pp. 91-108 ◽  
Author(s):  
Ghasem Afrouzi ◽  
M. Mirzapour ◽  
Vicenţiu Rădulescu
Keyword(s):  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Results ◽  
Existence And Multiplicity

Nonlinear Schrödinger equations involving exponential critical growth with unbounded or vanishing potentials

2022 ◽  
pp. 1-26
Author(s):  
J. Anderson Cardoso ◽  
Jonison Lucas Carvalho ◽  
Everaldo Medeiros
Keyword(s):  
Type Inequality ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Results ◽  
Nonlinear Schrödinger ◽  
Existence And Multiplicity ◽  
Nonlinear Schrodinger Equations ◽  
Exponential Critical Growth ◽  
Vanishing Potentials

In this paper we deal with the following class of nonlinear Schrödinger equations − Δ u + V ( | x | ) u = λ Q ( | x | ) f ( u ) , x ∈ R 2 , where λ > 0 is a real parameter, the potential V and the weight Q are radial, which can be singular at the origin, unbounded or decaying at infinity and the nonlinearity f ( s ) behaves like e α s 2 at infinity. By performing a variational approach based on a weighted Trudinger–Moser type inequality proved here, we obtain some existence and multiplicity results.

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