Multiple existence of solutions for a nonhomogeneous elliptic problem on RNRN

Let N≥3N≥3, 2∗=2N/(N−2)2∗=2N/(N−2) and p∈(2,2∗)p∈(2,2∗). Our purpose in this paper is to consider the multiple existence of solutions of problem −ε2Δu+u=|u|p−2u+λfu∈H1(RN), where ε,λ>0ε,λ>0, f∈L2(RN)∩C2(RN)f∈L2(RN)∩C2(RN), f≥0f≥0 and f≢0f≢0.We will show the effect of the shape of ff to the number of solutions.