Abstract We consider potential systems of differential equations of the form equation* - (u^) ^ = ᵤ F (t, u), in 0, T, equation* under the general boundary condition equation* ( (u^) (0), - (u^) (T) ) j (u (0), u (T) ), equation* where (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 -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.
Jebelean et al. (Mon,) studied this question.