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THE EXISTENCE OF INFINITELY MANY SO UTIONS OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS IN UNBOUNDED DOMAINS
Li Gongbao
Acta mathematica scientia,Series B. 1989, 9 (2):
175-188.
In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem
-Σi=1N∂/∂xi(|▽u|p-2∂u/∂xi)+a(x)|u|q-2u=f(x,u), x∈RN,N ≥ 2 u∈E{u∈Lq(R)N|u real,∂u/∂xi∈Lp(R)N,1 ≤ i ≤ N} where 2 ≤ p ≤ q,if N ≤ p;2 ≤ p ≤ q < Np/(N-p),if N > p.
where u|→∫RN F(x,u)dx(F(x,t)=∫0t f(x,s)ds) need not be compact operators from E to R1.
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