journal6 ›› 2000, Vol. 21 ›› Issue (1): 58-62.

• Scientific research bulletin • Previous Articles     Next Articles

The Shape of the Least Energy Solution of Quasilinear Elliptic Equations


  1. ( Institute of Mathematics and Software, Xiangtan Polytechnic University, Xiangtan 411201, Hunan China)
  • Online:2000-03-15 Published:2013-01-16

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

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