MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE

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MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE

MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE

MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE

MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE

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doi:10.1016/S0252-9602(08)60086-7

数学物理学报(英文版)

闫宝强

山东师范大学数学系, 济南 250014

收稿日期:2006-03-20 修回日期:2006-12-21 出版日期:2008-10-20 发布日期:2008-10-20
通讯作者: 闫宝强
基金资助:
Sponsored by the NNSFC (10571111) and the Fundation of Natural Science of Shandong Province (Y2005A07)

Yan Baoqiang

Department of Mathematics, Shandong Normal University, Jinan 250014, China School of Mathematics, Trinity College, Dublin 2, Ireland

Received:2006-03-20 Revised:2006-12-21 Online:2008-10-20 Published:2008-10-20
Contact: Yan Baoqiang

摘要：

The existence of at least two positive solutions is presented for the singular second-order boundary value problem

{(p(t)/1 (p(t)x’(t))′+Φ(t)f(t, x(t), p(t)x′(t))=0, 0 ＜t ＜1,

limt→0 p(t)x′(t)=0, x(1)=0.
by using the fixed point index, where f may be singular at x=0 and px’=0.

关键词: Boundary value problems, singularity, fixed point index

Abstract:

The existence of at least two positive solutions is presented for the singular second-order boundary value problem

{(p(t)/1 (p(t)x’(t))′+Φ(t)f(t, x(t), p(t)x′(t))=0, 0 ＜t ＜1,

lim_t→0 p(t)x′(t)=0, x(1)=0.
by using the fixed point index, where f may be singular at x=0 and px’=0.

Key words: Boundary value problems, singularity, fixed point index

中图分类号:

34B10

闫宝强. MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE[J]. 数学物理学报(英文版), 2008, 28(4): 851-864.

Yan Baoqiang. MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE[J]. Acta mathematica scientia,Series B, 2008, 28(4): 851-864.

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