西南石油大学学报(自然科学版) ›› 1990, Vol. 12 ›› Issue (4): 126-139.DOI: 10.3863/j.issn.1000-2634.1990.04.016

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NONTRIVIAL SOLUTION TO DIRICHLET PROBLEM OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH CRITICAL EXPONENT

Jiang Xiao-tao
  

  1. Dept. of Maths and Physics
  • Received:1990-03-09 Revised:1900-01-01 Online:1990-11-20 Published:1990-11-20

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Abstract:

In this paper, Dirichlet problemis discussed, in which ΩcR~N is a bounded domain and f(x,u)=O(|ul~(Q-2)u)(u→∞, Q=(NP)/(N-P), N>p≥2 The auther has proved that the psoblem (*) possesses a nontrivial weak solution under given conditions of a_1(x,s) and f(x,u).

Key words: Quasilinear elliptic equation, Critical exponent, Variational function, Theorem of mountain path, Concentration-compactness principle