Multiple solutions for an indefinite superlinear elliptic problem on RN

We study positive solutions of the equation −Δu=λu−a(x)up,x∈RN(N≥3), where p>1 is a constant, λ is a parameter and a(x) changes sign in a bounded domain. Under suitable conditions on the behavior of a(x) near its zero set and near |x|=∞, we obtain multiple positive solutions to this problem. Our approach is by approximating the problem with corresponding problems on enlarging balls. Our results improve and extend those of Du (2004) [15].