journal6 ›› 2000, Vol. 21 ›› Issue (1): 58-62.
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湖南省自然科学基金资助项目( 99JJY2003)
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摘要：讨论了方程- ?pu= - Div( | Du|p- 2Du)= Q( x ) | u|p*- 2u+ε | u| σ- 1u x∈Ω u|∂Ω= 0的极小能量解在ε→0时的形态: 当 ε→0时, 方程极小能量解 uε在测度意义下满足| Duε|p 弱Q-N- ppm SNp x0, | uε |p* 弱Q-Npm SNp x0,其中 Qm= maxx Q( x ) = Q( x 0) , x0为 x0 的 Dirac函数, Ω 是有界光滑区域.
关键词： 拟线性, 极小能量解, 集中紧原理
Abstract: This paper deals wi th the shape of the least energy solut ion of quasilinear el liptic equations involving criticale xponents- v pu = - Div( | Du|p- 2Du) = Q( x ) | u|p*- 2u+ E | u|R - 1u x I 8 ,u| 98= 0,where 8 is a bounded domain in RNwith smooth boundary 98, 0< E< K 1, and Ey 0. Q( x ) I C( 8) , RI [ 1, p*) .The fol lowing conclusions are proved:The least energy solution uE of the equat ions satisfies ( after passing to a subse -quence) :| DuE |p w Q-N- ppm SNpDx 0, as Ey 0, in the sense of measure.| uE |p* w Q-Npm SNpD x0, as Ey 0, in the sense of measure.Where Qm= maxx I 8Q( x ) = Q( x 0) , D x 0 be the Dirac mass at x 0, S is the bes t Sobolev cons tant.
Key words: quasilinear, the least energy solution, the concentration- compactness principle
曾宪忠, 熊之光. 临界拟线性椭圆方程极小能量解的形态[J]. journal6, 2000, 21(1): 58-62.
ZENG Xian-Zhong, XIONG Zhi-Guang. The Shape of the Least Energy Solution of Quasilinear Elliptic Equations[J]. journal6, 2000, 21(1): 58-62.
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https://zkxb.jsu.edu.cn/CN/Y2000/V21/I1/58
