Everaldo S. de Medeiros, Jose Anderson Cardoso, Manasses de Souza
Abstract:
We study a class of fractional Schrodinger equations of the form
where
is a positive parameter,
,
,
is the fractional Laplacian,
is a potential which may be
bounded or unbounded and the nonlinearity
is superlinear and
behaves like
at infinity for some
.
Here we use a variational approach based on the Caffarelli and Silvestre's
extension developed in [3] to obtain a nontrivial solution
for
sufficiently small.
Submitted September 16, 2016. Published March 20, 2017.
Math Subject Classifications: 35J20, 35J60, 35R11.
Key Words: Variational methods; critical points; fractional Laplacian.
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Everaldo S. de Medeiros Departamento de Matemática Universidade Federal da Paraíba, 58051-900 João Pessoa, PB, Brazil email: everaldomedeiros1@gmail.com | |
Jose Anderson Cardoso Departamento de Matemática Universidade Federal de Sergipe, 49000-100 São Cristóvão, Brazil email: anderson@mat.ufs.br | |
Manassés de Souza Departamento de Matemática Universidade Federal da Paraíba, 58051-900 João Pessoa, PB, Brazil email: manassesxavier@gmail.com |
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