含非线性梯度项的椭圆方程大解的渐近行为(Asymptotic behavior of large solution to elliptic problems with nonlinear gradient terms)

Abstract

By Karamata regular variation theory and the method of lower and supper solution, the boundary behavior of boundary blow-up solutions of the nonlinear elliptic equation Δu± | ▽u|q = b(x) f(u) in Ω，subject to the singular boundary condition u | ∂Ω =+∞ is investigated, where f grows at infinite, faster than any power up (p>1), b(x) ∈Cα (Ω) for some α>0，which is nonnogetive in Ω.

Keywords

• boundary blow-up
• nonlinear gradient terms
• karamata regular variation theory