Existence of blowup solutions for nonlinear problems with a gradient term

in a bounded domain. In the case f (u)= p(x)uγ, a > 0, and γ >max(1,a), Lair and Wood [7] dealt with the above equation in bounded domain and the whole space. They proved the existence of entire large solution under the condition ∫∞ 0 rmax|x|=r p(x)dr <∞ when the domain is RN . Recall that u is a large solution on a bounded domain Ω in RN , if u(x) → +∞ as dist(x,∂Ω) → 0, and u is called an entire large solution if u is defined on RN and lim|x|→+∞u(x)= +∞. Ghergu et al. [3] considered more general equation