带正对流项的一类非线性椭圆型方程爆炸解的存在性

Existence of Explosive Solutions for a Class of Nonlinear Elliptic Problem with a Positive Convection Term

应用摄动方法、上下解方法、单调性方法结合二阶椭圆型偏微分方程的估计方法得到了问题Δu=k(x) [up+｜ u｜q] ,x∈Ω ,u｜ Ω =+∞非负古典解的存在性 .其中Ω是RN 中的有界光滑区域 ,p >1 ,q∈ (1 ,2 ] ,k(x)在边界 Ω

WT5BZ]The considered equation is Δu=k(x)[u p+|u| q] on a smooth bounded domain Ω for p>1,q∈(1,2] and nonnegative continuous k(x) with property that k is not zero near Ω. The existence of a nonnegative solution u satisfying u| Ω =+∞ is proven.