Multiple solutions to relativistic systems with potential boundary conditions

We consider potential systems of differential equations of the form {equation*} -[ φ(u^{}) ] ^{} = ∇_u F(t,u), in [0,T],{equation*} under the general boundary condition {equation*} ( φ ( u)(0), -φ ( u)(T) )∈ ∂ j(u(0), u(T)),{equation*} where φ(y)=y/√1- |y|² and j:RN × RN → (-∞, +∞] is convex and lower semicontinuous. Making use of the variational approach introduced in the recent paper “Potential systems with singular φ -Laplacian”, we obtain multiplicity of solutions when the action functional is even, as well as existence of multiple geometrically distinct solutions when this functional is invariant with respect to some discrete group.