数学物理学报(英文版) ›› 1988, Vol. 8 ›› Issue (4): 431-448.
李工宝, 朱熹平
Li Gongbao Zhu Xiping
摘要： In this paper, we use the concentration-compactness prieciple togther with the Mountain Pass Lemma to get the existence of nontrivial solutions of the following scalar field equations with strong nonlinearity
-∑i=1N ∂/∂xi(|▽u|p-2 ∂u/∂xi)+a(x)|u|q-2 u=f(x,u),x∈RN,N ≥ 2 u∈E={u∈Lq(RN)|u real,∂u/∂xi∈Lp(RN),1 ≤ i ≤ N}, where 2 ≤ p ≤ q,p=N.