کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4666484 1345406 2012 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
چکیده انگلیسی

In this paper, we consider the following Dirichlet problem for poly-harmonic operators on a half space R+n:equation(1){(−Δ)mu=up,in R+n,u=∂u∂xn=∂2u∂xn2=⋯=∂m−1u∂xnm−1=0,on ∂R+n. First, under some very mild growth conditions, we show that problem (1) is equivalent to the integral equationequation(2)u(x)=∫R+nG(x,y)updy, where G(x,y)G(x,y) is the Greenʼs function on the half space.Then, by combining the method of moving planes in integral forms with some new ideas, we prove that there is no positive solution for integral equation (2) in both subcritical and critical cases. This partially solves an open problem posed by Reichel and Weth (2009) [40]. We also prove non-existence of weak solutions for problem (1).

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 229, Issue 5, 20 March 2012, Pages 2835–2867
نویسندگان
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