p-Laplacian算子型奇异方程组边值问题强正解存在性

The Existence of positive solutions of singulur boundary value systems with p-Laplacian

针对一类p-Laplacian算子型奇异方程组边值问题(φp(x′))′+a1(t)f(x(t),y(t))=0,(φp(y′))′+a2(t)g(x(t),y(t))=0,t∈(0,1),x(0)-β1x′(0)=0,x(1)-δ1x′(1)=0,y(0)-β2y′(0)=0,y(1)-δ2×y′(1)=0,建立了正解对(x,y)的存在性定理,与已有的结果不同,这里的正解对(x,y)满足,x(t)≥0,y(t)≥0,t∈J,x≠0,y≠0,这在生物共生关系中有实际意义.

In this paper, the author establishes the theorem on existence of strong positive solutions pair （x ,y） for a singular boundary value systems with p- Laplacian （φ,（x′））′＋α1（t）f（x（t）,y（t））=0,（φp（y′））′＋α2（t）g（x（t）,y（t））=0,t∈（0,1）,x（0）-β1x′（0）=0,x（1）-δ1x′（1）=0,y（0）-β2y′（0）=0,y（1）-δ2xy′（1）=0,where φ（x） =｜x｜=^P-2,p 〉 1, Different from the known results, tile pair of positive solutions （x ,y） here satisfies x（t）≥0,y（t）≥0,t∈J,x≠0,y≠0. This has the practical significance in the biological symbiosis relations.