Existence of Positive Solutions for Singular Second-order<Emphasis Type="Italic">m</Emphasis>-Point Boundary Value Problems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence of Positive Solutions for Singular Second-orderm-Point Boundary Value Problems

Authors:

Guo-wei?Zhang author-information" > author-information__contact u-icon-before" > mailto:gwzhangneum@sina.com" title=" gwzhangneum@sina.com" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Jing-xian?Sun

Affiliation:

(1) Department of Mathematics, Northeastern University, Shenyang, 110006, China;(2) Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, China

Abstract:

Abstract The singular second-order m-point boundary value problem

$left{ begin{aligned} & - {left( {Lvarphi } right)}{left( x right)} = h{left( x right)}f{left( {varphi {left( x right)}} right)},{kern 1pt} 0 < x < 1, & varphi {left( 0 right)} = 0,{kern 1pt} varphi {left( 1 right)} = {sumlimits_{i = 1}^{m - 2} {a_{i} varphi {left( {xi _{i} } right)}} } end{aligned} right.$

, is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ_i ∈ (0, 1) with 0 < ξ₁ < ξ₂ < · · · < ξ_m−2 < 1, a _i ∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions. Supported by the National Natural Science Foundation of China (No.10371066, No.10371013)

Keywords:

KeywordHeading" > Second-order singular equation multi-point boundary value problem positive solution cone fixed point index

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