奇异非线性椭圆边值问题正解的存在性

The Existence of Positive Solutions for Elliptic Boundary Value Problems with Singular Nonlinearity

本文将E.S.Noussair[4]的上下解方法推广到在u=0处可具奇性的半线性项f(x.u,Du)的椭圆边值问题,利用这个结果,得到球域外问题无穷多正解的存在性。当f(x.u.Du)=u^(-p)(P>0)时,证明了球域内问题的C^2(Ω)∩C^0(Ω)正解的存在唯一性。

In this paper, by the method of subsolution and supersolution ofNoussair[4], the existence of positive solutions for semilinear ellipticboundary value problem is discussed with singular nonlinear term f(x,u,Du)when u = 0. Using this result, the existence of infinitely many positivesolutions is obtained for the exterior problem of a ball and there is oneand only one positive solution for the interior problem of a ball whenf(x,u Du) = u^(-p)(p>0).