Nonlinear Schrödinger equations involving exponential critical growth with unbounded or vanishing potentials
Keyword(s):
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.
2001 ◽
Vol 159
(3)
◽
pp. 253-271
◽
2006 ◽
Vol 136
(5)
◽
pp. 889-907
◽
2014 ◽
Vol 58
(4)
◽
pp. 781-790
◽
2013 ◽
Vol 403
(2)
◽
pp. 680-694
◽
2019 ◽
Vol 198
(6)
◽
pp. 2093-2122
2013 ◽
Vol 33
(7)
◽
pp. 2911-2938
◽
Keyword(s):
2018 ◽
Vol 17
(1)
◽
pp. 143-161
◽
2010 ◽
Vol 9
(6)
◽
pp. 1723-1730
2021 ◽
Vol 60
(2)
◽