کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417042 | 1338514 | 2006 | 20 صفحه PDF | دانلود رایگان |
We consider functionals of the form Φ(u)=12â«RN|âu|2ââ«RNb(x)G(u) on D1,2(RN), Nâ¥3, whose critical points are the weak solutions of a corresponding elliptic equation in the whole RN. We present a Brezis-Nirenberg type result and a Hopf-type maximum principle in the context of the space D1,2(RN). More precisely, we prove that a local minimizer of Φ in the topology of the subspace V must be a local minimizer of Φ in the D1,2(RN)-topology, where V is given by V:={vâD1,2(RN):vâC(RN)withsupxâRNâ¡(1+|x|Nâ2)|v(x)|<â}. It is well-known that the Brezis-Nirenberg result has been proved a strong tool in the study of multiple solutions for elliptic boundary value problems in bounded domains. We believe that the result obtained in this paper may play a similar role for elliptic problems in RN.
Journal: Journal of Differential Equations - Volume 261, Issue 3, 5 August 2016, Pages 2006-2025