Multiplicity of solutions of variational systems involving φ-laplacians with singular φ and periodic nonlinearities

Using a Lusternik-Schnirelman type multiplicity result for some indefinite functionals due to Szulkin, the existence of at least n + 1 geometrically distinct T-periodic solutions is proved for the relativistic-type Lagrangian system Mathematical equation represented where φ is an homeomorphism of the open ball B a ⊂ ℝ n onto ℝ n such that φ(0) = 0 and φ = ∇, F is Tj-periodic in each variable qj and h ∈ L s(0; T;ℝ n) (s > 1) has mean value zero. Application is given to the coupled pendulum equations Mathematical equation represented Similar results are obtained for the radial solutions of the homogeneous Neumann problem on an annulus in ℝ n centered at 0 associated to systems of the form involving the extrinsic mean curvature operator in a Minkovski space