Asymptotic expansion of solutions to nonlinear elliptic eigenvalue problems
نویسندگان
چکیده
منابع مشابه
Asymptotic Expansion of Solutions to Nonlinear Elliptic Eigenvalue Problems
We consider the nonlinear eigenvalue problem −∆u+ g(u) = λ sinu in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 2) is an appropriately smooth bounded domain and λ > 0 is a parameter. It is known that if λ 1, then the corresponding solution uλ is almost flat and almost equal to π inside Ω. We establish an asymptotic expansion of uλ(x) (x ∈ Ω) when λ 1, which is explicitly represented by g.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2005
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-05-08114-1