On a planar non-autonomous Schrödinger–Poisson system involving exponential critical growth.

Albuquerque, F. S.; Carvalho, J. L.; Figueiredo, G. M.; Medeiros, E.

In this paper, we investigate the existence of solutions to the planar non-autonomous Schrödinger–Poisson system - Δ u V (| x |) u γ ϕ K (| x |) u = λ Q (| x |) f (u) , & x ∈ R 2 , Δ ϕ = K (| x |) u 2 , & x ∈ R 2 , where γ , λ are positive parameters, V, K, Q are continuous potentials, which can be unbounded or vanishing at infinity. By assuming that the nonlinearity f(s) has exponential critical growth, we derive the existence of a ground state solution to the system. A key feature of our approach is a new weighted Trudinger–Moser type inequality proved here.

Calculus of Variations & Partial Differential Equations, 2021, Vol 60, Issue 1, p1

0944-2669

Academic Journal

10.1007/s00526-020-01902-6