Infinite multiplicity of positive solutions of an inhomogeneous supercritical elliptic equation on RN

We are concerned with positive radial solutions of the inhomogeneous elliptic equation u+K (|x|) uᵖ+ f (|x|) =0 on RN, where N 3, >0 and K and f are nonnegative nontrivial functions. If K (r) r^, >-2, near r=0, K (r) r^, >-2, near r= and certain assumptions on f are imposed, then the problem has a unique positive radial singular solution for a certain range of. We show that existence of a positive radial singular solution is equivalent to existence of infinitely many positive bounded solutions which are not uniformly bounded, if p is between the critical Sobolev exponent pS () and Joseph-Lundgren exponent p₉₋ (). Using these theorems, we establish existence of infinitely many positive bounded solutions which are not uniformly bounded, for pS () -2.