一类非线性 Dirichlet 边值问题的正径向解

通过构造适当的锥并利用锥拉伸与锥压缩型的不动点定理研究了单位球上一类椭圆 Dirichlet 边值问题的正径向解的存在性, 其中非线性项可以是奇异的. 主要结论表明正径向解的存在性仅依赖于非线性项在其定义域的某个有界子集上的性质, 而与非线性项在此集合以外的性质无关.

Positive Radial Solution to a Class of Nonlinear Dirichlet Boundary Value Problems

By constructing a suitable cone and applying the fixed point theorem of cone expansion and compression type, the existence of positive radial solution is studied for a class of singular elliptic Dirichlet boundary value problems, where the nonlinear term may be singular. Main results show that the existence of positive radial solution depends only upon the properties of nonlinear term on a bounded subset of its domain, and the existence is independent of the properties of nonlinear term outside this set.