Nonlinear Schrödinger equation with unbounded or decaying radial potentials involving exponential critical growth inR2

• DOI: 10.1016/j.jmaa.2013.07.005
• Publication Date: 2013-08-07T13:00:55Z
• Authors: Francisco S.B. Al...; Claudianor O. Alves; Everaldo S. Medeiros
• Keywords: Multiplicity (mathematics)

Abstract We study the existence and multiplicity of solutions for the following class of nonlinear Schrodinger equations − Δ u + V ( ∣ x ∣ ) u = Q ( ∣ x ∣ ) f ( u ) in R 2 , where V and Q are unbounded or decaying radial potentials and the nonlinearity f ( s ) has exponential critical growth. The approaches used here are based on a version of the Trudinger–Moser inequality and a minimax theorem.