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Positive solutions for critical inhomogeneous elliptic problems in non-contractible domains

โœ Scribed by Haiyang He; Jianfu Yang

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
951 KB
Volume
70
Category
Article
ISSN
0362-546X

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๐Ÿ“œ SIMILAR VOLUMES

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In this paper, we deal with the conditions that ensure the existence of positive solutions for the singular elliptic equation -Au-tt(u/Ixl 2) = (lup\*(s)-2/Ixp)u + Nulq-2u with Dirichlet boundary condition. The results depend crucially on the parameters A, ~, and q.

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