Multiplicity results for nonhomogenous elliptic equation involving the generalized Paneitz-Branson operator

Abstract

"Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 without boundary ∂M, we consider the multiplicity result of solutions of the following nonhomogenous fourth order elliptic equation involving the generalized Paneitz-Branson operator, Pg (u) = f (x) |u|2 −2 u + h(x). Under some conditions and using critical points theory, we prove the existence of two distinct solutions of the above equation. At the end, we give a geometric example when the equation has negative and positive solutions. Keywords: Riemannian manifold, multiplicity result, nonhomogeneous, Paneitz-Branson operator, critical points theory."