【摘要】 应用摄动方法 ,古典上、下解方法 ,对含更广泛非线性项的问题 (P ) -Δu =k(x)f(u) - ｜ u｜q,x∈Ω ,u｜ Ω =+∞得到爆炸解的存在性 .特别允许非线性项的系数k(x)不仅在Ω的子区域上可恒为零 ,而且在Ω上适当无界 ;而对问题 (P+)Δu =k(x)f(u) +｜ u｜q,x∈Ω ,u｜ Ω =+∞仅得到了当k(x) ∈Cα( Ω)且k(x) >0 ,x∈ Ω时爆炸解的存在性 .更多还原

【Abstract】 By the perturbed method,and classical sub supersolutions method,for the more general nonlinearity about the problem of (P ) Δ u=k(x)f(u)-|u| q,x∈Ω,u| Ω =+∞,they obtain the existence of explosive solutions.In additon,they allow the coefficient of nonlinearity to be not only suitable unbounded on but also zero on large parts of inducing Ω.For the problem of (P+),the existence of explosive solution is obtained when k(x)∈C α() and k(x)>0.更多还原