数学物理学报(英文版) ›› 1992, Vol. 12 ›› Issue (3): 292-303.
薛儒英
Xue Ruying
摘要: We consider the nonlinear elliptic equation with mixed boundary conditions
(P)-△u=b(x)up+λu,u>0 for x∈Ω,u|Γ0=0,(∂u)/∂n|Γ1=0, where Ω is a smooth bounded domain in RN (N ≥ 3), whose boundary ∂Ω is made of two open sets Γ0 and Γ1,Γ0∩Γ1=ϕ, ∂Ω=Γ0∪Γ1,p=(N+2)/N-2. We prove the existence of a positive solution of (P)when b (x) and λ satisfy suitable conditions.