Existence of multiple positive solutions of subcritical semilinear elliptic problems in exterior strip domains

✍ Scribed by Tsing-San Hsu

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 257 KB
• Volume: 64
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.05.062

✦ Synopsis

In this paper, we consider the subcritical semilinear elliptic problem

(*) where 0, N 3, 1 < p < (N + 2)/(N -2), and is an exterior strip domain in R N . Under some suitable conditions on K and f , we show that there exists a positive constant * , * depending on K and f , such that ( * ) has exactly two solutions if ∈ (0, * ) and no solution if > * . Furthermore, if there exists a positive constant K 0 such that K(x) K 0 for x ∈ and f is bounded in , then ( * ) has at least one solution for = * .