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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 |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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