Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres

This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents (S-+/-epsilon):Delta(2)u-c(n)Delta u + d(n)u = Ku(n+4/n-4 +/-epsilon),u > 0 on S-n, where n >= 5,epsilon is a small positive parameter and K is a smooth positive function on S-n. We construct some solutions of (S-epsilon) that blow up at one critical point of K. However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation (S+epsilon).