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 Δ u+K(|x|)uᵖ+μ f(|x|)=0 on RN, where N≥ 3, μ>0 and K and f are nonnegative nontrivial functions. If K(r)~ rα, α>-2, near $r=0$, K(r)~ rβ, β>-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 μ. 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(α) and Joseph-Lundgren exponent pJL(α). Using these theorems, we establish existence of infinitely many positive bounded solutions which are not uniformly bounded, for pS(α)<p<pJL(α) if K(r)=r-α, α>-2.