Asymptotic Nondegeneracy of Least Energy Solutions to an Elliptic Problem with Critical Sobolev Exponent

Advanced Nonlinear Studies - Tập 8 Số 4 - Trang 783-797 - 2008
Futoshi Takahashi1
1Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

Tóm tắt

Abstract Consider the problem -∆u = N(N - 2)up + εk(x)u in Ω, u > 0 in Ω, u|∂Ω = 0 where Ω­ is a smooth bounded domain in ℝN (N ≥ 6), p = (N +2)/(N - 2), ε > 0 and k ∈ C2(Ω̅). Under certain assumptions, we prove the nondegeneracy of least energy solutions to the above problem as Ɛ →0. This is an extension of the recent work of Grossi [9].

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Tài liệu tham khảo

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Thông tin xuất bản

Advanced Nonlinear Studies

Tập 8 Số 4

783-797

Thông tin tác giả