Acta mathematica scientia,Series B ›› 1994, Vol. 14 ›› Issue (1): 64-74.
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Li Gongbao
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Abstract: 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=1N(∂)∂xi(|Du|p-2(∂u)/∂xi+a(x)|u|p-2u=f(x,u)+g(x),x∈Ω u∈W01,p(Ω) where N ≥ p ≥ 2 and Ω is a smooth domain in RN, f(x,u)~|u|p*-1 at u=∞ with p*=Np/(N-p), g(x) ∈ p' (Ω) with p'=p/(p-1).
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.
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