On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω= N\ω is an exterior domain in N, ω N is a bounded domain with smooth boundary, and N>2. μ 0, p>1 are some given constants. K(x) satisfies: K(x) Cαloc(Ω) and C, ε, M>0 such that K(x) C xl for any x M, with l −2−ε. Some existence and nonexistence of multiple solutions have been discussed under different assumptions on K.