Infinitely Many Positive Solutions For The Prescribed Curvature Equation In R~N

The prescribed scalar curvature problem is a classical problem in Riemannian ge-ometry.Let M be a Riemannian manifold,given f a smooth function on M,we can find a new metric by solving prescribed scalar curvature equation corresponding to M,such that the scalar curvature of the new metric is equal to f.Moreover the new metric is conformal to the standard metric on M.We consider the following prescribed scalar curvature type equation where Q(r)is a positive function;show that if Q(r)has the following expansion:there are constants ?>0,m>1,?>0,and Q0>0,such that then(0.2)has infinitely many non-radial positive solutions,whose energy can be made arbitrarily large.