Multiple existence of solutions for a nonhomogeneous elliptic problem on RNRN

Let N⩾3N⩾3, 2*=2NN−2 and p∈(2,2*)p∈(2,2*). Our purpose in this paper is to consider multiple existence of solutions of problem−Δu+u=|u|p−2u+f,u∈H1(RN), where f∈L2(RN)f∈L2(RN), f⩾0f⩾0 and f≢0f≢0.