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Positive solutions of some nonlinear elliptic problems in exterior domains

✍ Scribed by Vieri Benci; Giovanna Cerami


Publisher
Springer
Year
1987
Tongue
English
Weight
688 KB
Volume
99
Category
Article
ISSN
0003-9527

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The equation -Ξ΅ 2 u + a Ξ΅ (x)u = u p-1 with boundary Dirichlet zero data is considered in an exterior domain = R N \ Ο‰ (Ο‰ bounded and N 2). Under the assumption that a Ξ΅ a 0 > 0 concentrates round a point of as Ξ΅ β†’ 0, that p > 2 and p < 2N/(N -2) when N 3, the existence of at least three positive di

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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 ex