Three solutions for a Neumann partial differential inclusion via nonsmooth Morse theory (Q2359146)

Employing the nonsmooth critical point theory, the authors prove the existence of at least one positive and one negative solution to a partial differential inclusion involving a \(p\)-sublinear nonsmooth potential coupled with homogeneous Neumann boundary conditions. Furthermore, a third non-zero solution is determined by applying the nonsmooth Morse identity. The paper is closed by a remark regarding the possibility of producing a fourth solution of the mentioned partial differential inclusion.