کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899137 1631511 2017 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
New type of solutions to a slightly subcritical Hénon type problem on general domains
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
New type of solutions to a slightly subcritical Hénon type problem on general domains
چکیده انگلیسی
We consider the following slightly subcritical problem(℘ε){−Δu=β(x)|u|p−1−εuin Ω,u=0on ∂Ω, where Ω is a smooth bounded domain in Rn, 3≤n≤6, p:=n+2n−2 is the Sobolev critical exponent, ε is a small positive parameter and β∈C2(Ω‾) is a positive function. We assume that there exists a nondegenerate critical point ξ⁎∈∂Ω of the restriction of β to the boundary ∂Ω such that∇(β(ξ⁎)−2p−1)⋅η(ξ⁎)>0, where η denotes the inner normal unit vector on ∂Ω. Given any integer k≥1, we show that for ε>0 small enough problem (℘ε) has a positive solution, which is a sum of k bubbles which accumulate at ξ⁎ as ε tends to zero. We also prove the existence of a sign changing solution whose shape resembles a sum of a positive bubble and a negative bubble near the point ξ⁎.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 263, Issue 11, 5 December 2017, Pages 7221-7249
نویسندگان
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