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

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

Acta mathematica scientia,Series B

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

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

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Abstract

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

CLC Number:

34B10

Cite this article

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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URL: http://actams.apm.ac.cn/sxwlxbB/EN/10.1016/S0252-9602(08)60086-7

http://actams.apm.ac.cn/sxwlxbB/EN/Y2008/V28/I4/851

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