In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2008 ( 2008), p. 1-6
Abstract:
We prove that the semilinear elliptic equation − Δ u = f ( u ) , in Ω , u = 0 , on ∂ Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μ t q ≤ f ( t ) ≤ C t p at infinity and behaves like t q near the origin, where 1 〈 q 〈 ( N + 2 ) / ( N − 2 ) if N ≥ 3 and 1 〈 q 〈 + ∞ if N = 1 , 2 . In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of p .
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2008
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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