On singular Q-curvature type equations

Abstract

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.

Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds

“…The latter consists in the search for solutions to fourth-order elliptic equations with critical exponents in the sense of the Sobolev inclusions. We refer the reader to the works by Benalili [4], Chang [8], Chang-Yang [9], Djadli-Hebey-Ledoux [10], Djadli-Malchiodi-Ould Ahmedou [12], [13], Esposito-Robert [15], Felli [16], Hebey-Robert [17], Lin [21], Robert [24], [25], to quote only few of them.…”

On singular elliptic equations involving critical Sobolev exponent

“…Now, we use the following Hardy-Sobolev inequalities proven in [5] (the Hardy-Sobolev inequalities for the singular Yamabe equation was proven in [9]). …”

“…Theorem 12 [5] Let (M, g) be a compact 5 ≤ n-dimensional Riemannian manifold and p, q and γ three real numbers satisfying…”

Second-Order Elliptic Equation with Singularities

“…Traditionally, to obtain solutions of equation ( 1), we will use, when necessary, ideas developed in [9,11,18], and we will use classical variational techniques by minimizing the functional F. However, serious difficulties appear compared with the smooth case. In order, we define the quantity…”