|Table of Contents|

Existence of Positive Solutions for Semi-Positone n Order∞-Point Boundary Value Problem(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2019年01期
Page:
6-
Research Field:
·数学·
Publishing date:

Info

Title:
Existence of Positive Solutions for Semi-Positone n Order∞-Point Boundary Value Problem
Author(s):
Shen Wenguo1; Sun Jianren2
(1.Department of Basic Courses,Lanzhou Institute of Technology,Lanzhou 730050,China)(2.College of Mechano-Electronic Engineering,Lanzhou Institute of Technology,Lanzhou 730050,China)
Keywords:
n-order ∞-point semi-positone boundary value problem; Green function; positive solutions; fixed point theorem in cones
PACS:
O175
DOI:
10.3969/j.issn.1001-4616.2019.01.002
Abstract:
In this paper,we study the existence of positive solutions for semi-positone n order ∞-point boundary value problem x(n)(t)+λf(t,x(t))=0,0<t<1,x(0)=∑∞i=1αix(ξi),x’(0)=…=x(n-2)(0)=0,x(1)=∑∞i=1βix(ηi),where ξi,ηi∈(0,1)(i=1,2,…),satisfing 1>ξ1>ξ2>…>ξn>…>0,0<η1<η2<…<ηn<…<1,αi,βi∈(0,∞)satisfing 0< ∑∞i=1αi(1-ξn-1i)<1,0<∑∞i=1βiηn-1i<1,and D∞=∑∞i=1αiξn-1i(1-∑∞i=1βi)+(1-∑∞i=1βiηn-1i)(1-∑∞i=1αi)>0. We study the existence of positive solutions for the above problem. The proof of our main result is based upon a fixed point theorem in cones.

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Last Update: 2019-03-30