THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (1): 64-74.

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

李工宝

Inst. of Math. Sci., The Chinese Academy of Sciences, Wuhan 470071, China

收稿日期:1992-03-09 出版日期:1994-03-25 发布日期:1994-03-25
基金资助:
Partially supported by Youth's Foundation NSFCS.

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

Li Gongbao

Inst. of Math. Sci., The Chinese Academy of Sciences, Wuhan 470071, China

Received:1992-03-09 Online:1994-03-25 Published:1994-03-25
Supported by:
Partially supported by Youth's Foundation NSFCS.

摘要/Abstract

摘要： In this paper, the existence of a weak solution to the following elliptic equation with critical Soboiev exponent on unbounded domain Ω is proved
-∑_t=1^N(∂)∂x_i(|Du|^p-2(∂u)/∂x_i+a(x)|u|^p-2u=f(x,u)+g(x),x∈Ω u∈W₀^1,p(Ω) where N ≥ p ≥ 2 and Ω is a smooth domain in R^N, f(x,u)~|u|^{p^*-1} at u=∞ with p^*=Np/(N-p), g(x) ∈ p' (Ω) with p'=p/(p-1).

李工宝. THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN[J]. 数学物理学报(英文版), 1994, 14(1): 64-74.

Li Gongbao. THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN[J]. Acta mathematica scientia,Series B, 1994, 14(1): 64-74.

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

THE EXISTENCE OF A WEAK SOLUTION OF QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL SOBOLV EXPONENT ON UNBOUNDED DOMAIN

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