Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on RNRN

Let N≥3N≥3, 2∗=2N/(N−2)2∗=2N/(N−2). Our purpose in this paper is to consider the existence and multiplicity of solutions of the problem {−Δu=|u|2∗−2u+fon RNu∈H1(RN) where f∈L2∗/(2∗−1)(RN)∩L∞(RN),f≥0f∈L2∗/(2∗−1)(RN)∩L∞(RN),f≥0 and f≢0f≢0.