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We 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.

Key words Hamiltonian elliptic systems, exponential critical growth, Trudinger-Moser inequality MSC (2010) 35A23, 35B33, 35J50, 35J92This paper is concerned with the existence of solutions for a class of Hamiltonian elliptic systems with unbounded, singular or decaying radial potentials and nonlinearities having exponential critical growth. The approach relies on an approximation procedure and a version of the Trudinger-Moser inequality.