一类非线性椭圆型问题爆炸解的存在性与全局最优估计

Existence and Global Optimal Asymptotic Behaviour of Large Solutions to a Semilinear Elliptic Problem

设f满足:H(t)=∫t∞f(dss)<∞,t∈R,∫-∞∞f(dss)=∞(或H(t)=∫t∞f(dss)<∞,t>0,∫0∞f(dss)=∞,且f'(t)∫t∞f(dss)在R(或(0,∞))上有界,构造爆炸上解和爆炸下解,得到了非线性椭圆型问题Δu=f(u),x∈Ω,u|Ω=+∞解的存在性和渐近行为的全局最优估计.

Abstract： By constructing an explosive subsolution and an explosive supersolution, it has been shown for the existence and the estimate of global optimal asymptotic behaviour of large solutions to the nonlinear elliptic problem Au =f（u）;u｜aΩ=＋∞ under the new constructive conditions on f： H（t） =∫^∞ t ds /f（s）〈∞,t∈R,∫^∞ -∞ ds/f（s）=∞（or H（t）==∫^∞ 1 ds/f（s）〈∞ ,t〉0,∫^∞ 0 ds/f（s）=∞ .and f（t）∫^∞ t ds/f（s） is bounded on R （or （0,∞）.