Existence and multiplicity results for the fractional magnetic Schrödinger equations with critical growth

2021 ◽  
Vol 62 (6) ◽  
pp. 061503
Author(s):  
Ya-Hong Guo ◽  
Hong-Rui Sun ◽  
Na Cui
Keyword(s):  
Critical Growth ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Results ◽  
Existence And Multiplicity

An Elliptic Equation Involving Exponential Critical Growth in ℝ2

2015 ◽  
Vol 15 (1) ◽  
Author(s):  
Francisco S. B. Albuquerque ◽  
Everaldo S. Medeiros
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Functional Space ◽  
Critical Growth ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Existence And Multiplicity ◽  
Minimax Methods ◽  
Exponential Critical Growth

AbstractWe study the following class of nonhomogeneous Schrödinger equations−Δu + V(|x|)u = Q(|x|) f(u) + h(x) in ℝwhere V and Q are unbounded or decaying radial potentials, the nonlinearity f (s) has exponential critical growth and the nonhomogeneous term h belongs to the dual of an appropriate functional space. By combining minimax methods and a version of the Trudinger-Moser inequality, we establish the existence and multiplicity of weak solutions for this class of equations.

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.

Sign in / Sign up

Export Citation Format

Share Document