Schr?dinger–Maxwell systems on compact Riemannian manifolds

摘要

In this paper, we are focusing to the following Schr?dinger–Maxwell system: ( ??gu + β(x)u + euφ = Ψ(λ, x)f(u) in M, ??gφ + φ = qu2 in M, (SMe Ψ(λ,·) ) where (M, g) is a 3-dimensional compact Riemannian manifold without boundary, e, q > 0 are positive numbers, f : R → R is a continuous function, β ∈ C ∞(M) and Ψ ∈ C ∞(R+ × M) are positive functions. By various variational approaches, existence of multiple solutions of the problem (SMe Ψ(λ,·) ) is established.