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A ROBIN BOUNDARY PROBLEMWITH HARDY POTENTIAL AND CRITICAL NONLINEARITIES

机译:罗宾边界问题难解性和临界非线性

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摘要

Let be a bounded domain with a smooth C2 boundary in Rn (n 3), 0 2 ˉ, and denote the unit outward normal to @. In this paper, we are concerned with the following class of boundary value problems where 2 = 2n/(n 2) is the limiting exponent for the embedding of H1() into Lp(), 2 < p < 2, μ < ˉμ , (N2)2 4 , 0 and 2 R1 are parameters, and (x) 2 C(@), (x) 0. Through a compactness analysis of the functional corresponding to the problem (), we obtain the existence of positive solutions for this problem under various assumptions on the parameters μ, and the fact that 0 2 or 0 2 @.
机译:设Rn(n 3)为0 2且C2边界光滑的有界域,并表示垂直于@的单位。在本文中,我们关注以下几类边值问题,其中2 = 2n /(n 2)是将H1()嵌入Lp()的极限指数,2 <2,μ<ˉμ, (N2)2 4,0和2 R1是参数,而(x)2 C(@),(x)0。通过对与问题()对应的函数的紧致性分析,我们获得了正解存在这个问题是在各种假设下对参数μ以及0 2或0 2 @进行的。

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