ON PRESCRIBING SCALAR CURVATURE PROBLEM ON S-3 AND S-4

We show that for the prescribing scalar curvature problem on S(n) (n - 3, 4), we can perturb any given positive function in any neighborhood of any given point such that for the perturbed function there exist as many solutions as we want to the prescribing scalar curvature equation on S(n) (n = 3, 4). Critical exponent equations DELTA-u - K (x) u(n+2)/(n-2) in R(n) (n = 3, 4) with K (x) > 0 being periodic in one of the variables are also studied and infinitely many positive solutions (modulo translations by its periods) are obtained under some additional mild hypotheses on K (x).