Emden-Fowler方程奇异边值问题的定号解

Signed Solutions of Emden-Fowler Equation Singular BVPS

本文研究Emden-Fowler方程奇异边值问题{ü=-q{x)|u|^(p-2)u+λu,x∈(0,1),u(0)=u(1)=0,的定号解.本文允许问题(1)可以在一个零测度集上存在奇异性,即允许在无穷多个点处奇异;另外,多数文献得到的定号解是正解,本文证明了问题(1)至少有一正解和一个负解.

This paper is devoted to the existence of signed solutions of a class of Emden-Fowler equation singular BVPS （1）. We focus on the case that the nonlinear term has infinite many singular points. Different from the literature, we obtain one positive solution and one negative solution of problem （1）.