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Abstract
In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=RN\\ω is an exterior domain in RN, ω⊂RN 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|x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and nonexistence of multiple solutions have been discussed under different assumptions on K.
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