一类非线性椭圆方程正爆破解的存在性

研究了如下的非线性椭圆方程正爆破解存在性：{△u＋g（x）u^a│△↓u│q=ρ（x）f（u），x∈Ω；其中Ω R^N（N≥3）。其中QCR“（N≥3）是一个C^2类有界区域或者Ω=R^N，a≤0，q∈0，2]。运用上下解定理和摄动方法，得到了若干正爆破解存在的充分性条件，并就解存在的必要性做了论证。

Existence of Explosive Positive Solutions of a Class of Nonlinear Elliptic Problems

In this paper the problem of nonlinear equation：{△u＋g（x）u^a│△↓u│q=ρ（x）f（u）,x∈Ω;is considered, where Ω R^N（N≥3）is either a C^2 bounded domain or equal to Ω=R^N,a≤0,q∈0,2].Some sets of suitable conditions are given by using the explosive super-subsolution method , the inner estimation theory and the perturbed technique, which guarantee, respectively, the existence of explosive positive solutions . Meanwhile, a necessary condition is given.