A Variational Approach for the Neumann Problem in Some FLRW Spacetimes

Abstract

In this paper, we study, using critical point theory for strongly indefinite functionals, the Neumann problem associated to some prescribed mean curvature problems in a FLRW spacetime with one spatial dimension. We assume that the warping function is even and positive and the prescribed mean curvature function is odd and sublinear. Then, we show that our problem has infinitely many solutions. The keypoint is that our problem has a Hamiltonian formulation. The main tool is an abstract result of Clark type for strongly indefinite functionals.

Keywords

• quasilinear elliptic equation
• critical point theory
• hamiltonian systems
• flrw spacetime
• prescribed mean curvature
• neumann problem
• 35j25
• 58e05
• 70h05
• 53c42
• 53c50