数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (2): 124-138.
周焕松
Zhou Huansong
摘要: Let f(x, t):R2×R→ R be a C2-function with respect to t∈R, f(x,0)=0, f(x, t)~ebt2 as t→+∞ for somc b>0. Under suitable conditions on f(x, t), author shows that for g∈L2 (R2), g(x) ≥ (≠) 0, the following semilinear clliptic problem:
-△u+u=f(x,u)+λg(x),x∈R2, u∈H1(R2),λ>0,
has at least two distinct positive solutions for any λ∈(0, λ*), at least one positive solution for any λ∈[λ*, λ*] and has no positive solntion for all λ>λ*. It is also proved that λ* ≤ λ*< +∞.