[1]沈文国,孙建仁.高阶无穷多点半正边值问题正解的存在性[J].南京师范大学学报(自然科学版),2019,42(01):6.[doi:10.3969/j.issn.1001-4616.2019.01.002]
　Shen Wenguo,Sun Jianren.Existence of Positive Solutions for Semi-Positone n Order∞-Point Boundary Value Problem[J].Journal of Nanjing Normal University(Natural Science Edition),2019,42(01):6.[doi:10.3969/j.issn.1001-4616.2019.01.002]
点击复制

高阶无穷多点半正边值问题正解的存在性()
分享到：

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

卷:
第42卷
期数:
2019年01期
页码:
6
栏目:
·数学·
出版日期:
2019-03-20

文章信息/Info

Title:
Existence of Positive Solutions for Semi-Positone n Order∞-Point Boundary Value Problem
文章编号:
1001-4616(2019)01-0006-08
作者:
沈文国1; 孙建仁2
(1.兰州工业学院基础学科部,甘肃 兰州 730050)(2.兰州工业学院机电工程学院,甘肃 兰州 730050)
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)
关键词:
n阶无穷多点半正边值问题; 格林函数; 正解; 推广的锥上不动点定理
Keywords:
n-order ∞-point semi-positone boundary value problem; Green function; positive solutions; fixed point theorem in cones
分类号:
O175
DOI:
10.3969/j.issn.1001-4616.2019.01.002
文献标志码:
A
摘要:
研究二阶无穷多点半正边值问题: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)正解的存在性问题.其中ξi,ηi∈(0,1)(i=1,2,…),1>ξ1>ξ2>…>ξn>…>0,0<η1<η2<…<ηn<…<1,αi,βi∈(0,∞),0<∑∞i=1αi(1-ξn-1i)<1,0<∑∞i=1βiηn-1i<1且D∞=∑∞i=1αiξn-1i(1-∑∞i=1βi)+(1-∑∞i=1βiηn-1i)(1-∑∞i=1αi)>0. 我们给正参数λ和函数f(t,x(t))赋予一定的条件,使得上述问题至少存在一个正解.本文应用锥上不动点定理来证明主要定理.
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.

参考文献/References:

[1] PAUL W E,BASHIR A. Positive solutions of a nonlinear n-th order boundary value problem with nonlocal conditions[J]. Applied mathematics letters,2005,18(5):521-527.
[2]GUO Y P,JI Y D,ZHANG J H. Three positive solutions for a nonlinear n-th order m-point boundary value problem[J]. Nonlinear analysis:TMA,2008,68(11):3485-3492.
[3]JI Y D,GUO Y P. The existence of countably many positive solutions for some nonlinear n-th order m-point boundary value problems[J]. Journal of computational and applied mathematics,2009,232(2):187-200.
[4]YANG J B,WEI Z L. Positive solutions of n-th order m-point boundary value problem[J]. Applied mathematics and computation,2008,202(2):715-720.
[5]PANG C C,DONG W,WEI Z L. Green’s function and positive solutions of n-th order m-point boundary value problem[J]. Applied mathematics and computation,2006,182(2):1231-1239.
[6]GRAEF J R,YANG B. Positive solutions to a multi-point or nonlinear higher order boundary value problem[J]. Journal of mathematical analysis and applications,2006,316(2):409-421.
[7]GRAEF J R,MOUSSAOUI T. A Class of n-point boundary value problem[J]. Applied mathematics and computation,2006,182(2):1231-1239.
[6]GRAEF J R,YANG B. Positive solutions to a multi-point or nonlinear higher order boundary value problem[J]. Journal of mathematical analysis and applications,2006,316(2):409-421.
[7]GRAEF J R,MOUSSAOUI T. A Class of order BVPs with nonlocal conditions[J]. Computers and mathematica applications,2009,58(8):1662-1671.
[8]WEBB J R L. Nonlocal conjugate type boundary value problem of higher order[J]. Nonlinear analysis:TMA,2009,71(5/6):1933-1940.
[9]MA Q Z,DU R J. Existence of positive solutions for semipositine multi-point boundary-value problems[J]. Journal of Lanzhou university(natural sciences),2007,43(5):98-100.
[10]ZHAI C B. Existence of positive solutions for semipositine three-point boundary value problems[J]. Journal of computational and applied mathematics,2009,228(1):279-286.
[11]MA R. Multiple positive solutions for a semipositine four-order boundary value problem[J]. Hiroshima Math J,2003,33(2):217-227.
[12]ANURADHA V,HAI D D,SHIVAJI R. Existence results for superlinear semipositine BVP’S[J]. Proceedings of the American mathematical society[J]. 1996,124(3):757-763.
[13]沈文国. 二阶无穷多点半正边值问题正解的存在性问题[J]. 华中师范大学学报(自然科学版),2013,47(2):145-149.
[14]SUN J,WEI J. Existence of positive solutions for semipositine second order three-point boundary value problem[J]. Electronic journal of differential equations,2008,79(41):1-7.
[15]GUO D,LAKSHMIKANTHAM V. Nonlinear problems in abstract cones,vol. 5 of notes and reports in mathematics in science and engineering[M]. Boston,Mass,USA:Academic Press,1988.
[16]ZHANG G W,SUN J X. A generalization of the cone expansion and compression fixed point theorem and applications[J]. Nonlinear Anal:TMA,2007,67(2):579-586.

相似文献/References:

[1]江成顺.反应扩散模型解的爆破与避免爆破[J].南京师范大学学报(自然科学版),2018,41(01):9.[doi:10.3969/j.issn.1001-4616.2018.01.003]
　Jiang Chengshun.Blow-up of Solutions and Avoidance of Blow-up forSome Reaction Diffusion Models[J].Journal of Nanjing Normal University(Natural Science Edition),2018,41(01):9.[doi:10.3969/j.issn.1001-4616.2018.01.003]

备注/Memo

备注/Memo:
收稿日期:2017-05-01.
基金项目:国家自然科学基金(11561038)、 兰州工业学院‘开物’科研创新团队支持计划资助(2018KW-03).
通讯联系人:沈文国,教授,博士,研究方向:非线性微分方程. E-mail:shenwg369@163.com
更新日期/Last Update: 2019-03-30