This paper is devoted to Q-curvature type equations with singularities; mainly we give existence and regularity results of solutions. To have positive solutions which will be meaningfully in conformal geometry we restrict ourself to special manifolds.2000 Mathematics Subject Classification. Primary 58J05.

Abstract. This paper deals with a fourth order elliptic equation on compact Riemannian manifolds, the function f involved in the nonlinearity is of changing sign which makes the analysis more difficult than the case where f is of constant sign.We prove the multiplicity of solutions in the subcritical case which is the subject of the first theorem. In the second one we establish the existence of solutions to the equation with critical Sobolev growth.

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Abstract. This paper deals with the existence of solutions to a class of fourth order nonlinear elliptic equations. The technique used relies on critical points theory. The solutions appeared as critical points of a functional restricted to a suitable manifold. In the case of constant coefficients we obtain the existence of three distinct solutions.