The non-existence results for a class of integral equation

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	The non-existence results for a class of integral equation
	Xu, Jiankai ; Wu, Huoxiong ; Tan, Zhong ; Wu HX(伍火熊) ; Tan Z(谭忠)
刊名	http://dx.doi.org/10.1016/j.jde.2013.12.009
	2014-03-01
英文摘要	National Natural Science Foundation of China [11071200, 11126148, 1127130, 11371295]; Young Foundation of Hunan Agriculture University [12QN08]; Scientific Research Fund of Hunan Provincial Education Department [13C395]; In this paper, we consider the following integral system u(x, b) = integral(Rn) u(q)(y, b)/(b + vertical bar x - y vertical bar(lambda) dy, (0.1) which is related to the weak type convolution-Young's inequality. Under the assumption of that lambda is an element of (0, n) and 0 < q <= n/lambda, we show that system (0.1) doesn't have a positive solution in L-loc(q)(R-n). Furthermore, we prove that as lambda is an element of (0, n - 1/3) and q = 2n/lambda - 1, system (0.1) does not admit positive solution in Lq+1(R-n) (n > 2), which implies that the maximizing pair of the weak type convolution-Young's inequality with kernel function (b + vertical bar x vertical bar)(-lambda) does not exist. Meanwhile, for lambda is an element of (-infinity, 0) and q = 2n/lambda - 1, we also show that the system (0.1) doesn't admit non-negative Lebesgue measurable solution. This is distinct from the original conformal invariant integral system. (C) 2013 Elsevier Inc. All rights reserved.
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91363]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Xu, Jiankai,Wu, Huoxiong,Tan, Zhong,et al. The non-existence results for a class of integral equation[J]. http://dx.doi.org/10.1016/j.jde.2013.12.009,2014.
APA	Xu, Jiankai,Wu, Huoxiong,Tan, Zhong,伍火熊,&谭忠.(2014).The non-existence results for a class of integral equation.http://dx.doi.org/10.1016/j.jde.2013.12.009.
MLA	Xu, Jiankai,et al."The non-existence results for a class of integral equation".http://dx.doi.org/10.1016/j.jde.2013.12.009 (2014).