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: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*< +∞.
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