Zhi Jun ZHANG(1),Shuang Ping T
They consider the semilinear problems △u=k(x)f(u), u>0, x∈Ω, u| Ω=∞, where Ω a bounded domain with C2 boundary Ω in RN (N≥3), f is a nonneg-ative, nondecreasing C1 function satisfying f'(a)∫a∞1/f(s)ds≤C0, a > 0. The new change of variable w(x) =∫u(x)∞ds/f(s) transforms the problems of explosive solutions into the equivalent singular Dirichlet problems. They expose that the explosive solutionshave the lowest speed and the two models of explosive problems are basically the one. Then, by the perturbed method, and sub - supersolutions method, the existence of explosive solutions is obtained. In addition, They allow k to be not only suitable unbounded on Ω but also zero on large parts of Ω including Ω. They also show that the problems have one entire solution and characterize the asymptotic behavior of the solution near ∞ when Ω= RN(see [1-33]).
