具p-Laplacian算子型奇异方程组边值问题正解的存在性

本文讨论了一类具p-Laplacian算子型奇导方程组边值问题(φp(x'))'+α1(t),f(x(t),y(t))=0,(φp(y'))'+α2(t)g(x(t),y(t))=0,x(0)-β1x'(0)=0,x(1)+δ1x'(1)=0,y(0)-β2Y'(0)=0,y(1)+δ2y'(1)=0正解的存在性,其中φp(x)=|x|p-2x,p>1.通过使用不动点指数定理,在适当的条件下,建立了这类奇异方程组边值问题存在一个或者多个正解的充分条件.这些结果能用来研究椭圆型方程组边值问题径向对称解的存在性.

The Existence of Positive Solutions of Singular Boundary Value Systems with p-Laplacian

In this paper, we discuss the existence of positive solutions for a singular boundary value systems with p-Laplacian (φp(x'))' + α1　(t)f(x(t),y(t)) = 0, (φp(y'))' +α2(t)g(x(t),y(t)) = 0, x(0) - β1x'(0) = 0, x(1) +δx'(1) = 0, y(0) - β2y'(0) = 0, y(1) + δ2y'(1) = 0, where φp(x) = |x|p-2x, p > 1. By using the fixed-point index theorem, the sufficient conditions of the existence of one or multiple positive solutions for the boundary value systems under some conditions are established. These results can be applied to the study of the existence of the radial solutions for the elliptic boundary value systems.