Multiple positive solutions for an inhomogeneous semilinear problem in exterior domains

✍ Scribed by Yinbin Deng; Yujin Guo

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 305 KB
• Volume: 66
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.01.023

✦ Synopsis

This paper is a contribution on the inhomogeneous problem

where Ω = R N \ω is an exterior domain in R N , ω ⊂ R N is a bounded domain with a smooth boundary and N > 2. λ > 0, μ > 0 and p > 1 are given constants. f (x) ∈ L ∞ (Ω ) and K (x) are given locally Hölder continuous functions in Ω , and K (x) satisfies a fast decay condition: ∃C, , M > 0 such that |K (x)| ≤ C|x| l for any |x| ≥ M with l ≤ -2 -. By applying the monotone iteration method and the Mountain Pass Lemma, some results on the existence and nonexistence of multiple solutions are discussed under different assumptions for K (x) and f (x).