具p-Laplacian算子型奇异边值问题多重正解

MULTIPLE POSITIVE SOLUTIONS OF SINGULAR BOUNDAY VALUE PROBLEMS WITH p-LAPLACIAN

本文讨论了一类具ｐ－Ｌａｐｌａｃｉａｎ算子型奇异边值问题（φｐ（ｘ＇））＇＋ａ（ｔ）ｆ（ｘ（ｔ））＝０，ｘ（０）－βｘ（０′）＝ ０，ｘ（１）＋ δｘ′（１）＝０多重正解的存在性，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，建立了这类边值问题存在多重正解的充分条件．这些结果能被用来研究椭圆边值问 题多重径向对称解的存在性．

The authors discuss the existence of multiple positive solutions for a singular boundary value problems with p-Laplacian (φｐ(x'))'+a(t)f(x(t)) = 0, x(0)-βx'(0) = 0, x(1)+δx'(1) = 0, where, φp(x) = |x|p-2x, p > 1. By using the fixed-point index theorem, the sufficient conditions of the existence of multiple positive solutions for the boundary value problems under some conditions are established. These results can be applied to studying the existence of the multiple radial solutions for the elliptic boundary value problems.