On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains
نویسندگان
چکیده
In this paper, we study the existence and nonexistence of multiple positive solutions for problem ∆u+K(x)up = 0 in Ω. u > 0 in Ω, u ∈ H1 loc(Ω) ∩ C(Ω). u ∣∣ ∂Ω = 0, u → μ > 0 as |x| → ∞ 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) ∈ Cα loc(Ω) and ∃C, ,M > 0 such that, |K(x)| ≤ C|x|l for any |x| ≥ M, with ∗Research supported by the Natural Science Foundation of China
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