一类奇异p-Laplace微分方程正解的存在性与不存在性

Existence and Nonexistence of Positive Solutions to a Singular $p$-Laplacian Differential Equation

中文关键词:  p-Laplace微分方程  奇性  正解  存在性  不存在性.

英文关键词:$p$-Laplacian  singularity  positive solution  existence  nonexistence.

中文摘要:

      本文给出了一类奇异p-Laplace微分方程在某一函数类中正解存在性的充分必要条件.利用上、下解方法和紧技巧,能够证明存在性,而证明不存在性的方法涉及到单调技巧.

英文摘要:

      In this paper we give a necessary and sufficient condition for the existence of positive solutions for the one-dimensional singular $p$-Laplacian differential equation. The methods used to show existence rely on upper-lower solutions method and compactness techniques, while the methods used to prove nonexistence are based on monotone techniques and scaling arguments.