数学物理学报(英文版) ›› 1994, Vol. 14 ›› Issue (S1): 40-45.
姜明
Jiang Ming
摘要: The existence of positive solutions to the semlinear elliptic boundary value problem
-Δ=f(x,u) in Ω and u=0 on ∂Ω is studied in this paper. The result obtained differs from the other known results in that the positivity of the solution does not follow from the positivity of f.Our result roughly says that if Ω is not too wide in some one direction, there is always a positive solution even if f changes signs, which is proved using the so-calles sub-super solution approach.