Multiple solutions and profile description for a nonlinear Schrödinger–Bopp–Podolsky–Proca system on a manifold

We prove a multiplicity result for {-epsilon(2) Delta(g)u + omega u + q(2) phi u = vertical bar u vertical bar(p-2) u in M, -Delta(g)phi + a(2)Delta(2)(g)phi + m(2)phi = 4 pi u(2) where (M, g) is a smooth and compact 3-dimensional Riemannian manifold without boundary, p is an element of (4, 6), a, m, q not equal 0, epsilon > 0 small enough. The proof of this result relies on Lusternik-Schnirellman category. We also provide a profile description for low energy solutions.