带
Existence of negative convex solutions for a discrete mixed boundary value problem with
- 中山大学学报(自然科学版)(中英文) 2023年62卷第6期 页码：171-176
- 作者机构：
西北师范大学数学与统计学院， 甘肃 兰州 730070
- 作者简介：
赵亚丽（1997年生），女；研究方向：差分方程及其应用；E-mail：zylZYL19970807@163.com
陈天兰（1986年生），女；研究方向：差分方程及其应用；E-mail：tianlan_chen@nwnu.edu.cn
- 基金信息：国家自然科学基金青年基金(11801453;11901464);甘肃省青年科技基金计划项目(20JR10RA100)
DOI：10.13471/j.cnki.acta.snus.2021A077
中图分类号： O175.7纸质出版日期：2023-11-25，
网络出版日期：2023-10-27，
收稿日期：2021-09-17，
录用日期：2022-07-10
扫 描 看 全 文
赵亚丽,陈天兰.带p-Laplace算子的离散混合边值问题负凸解的存在性[J].中山大学学报(自然科学版),2023,62(06):171-176.
ZHAO Yali,CHEN Tianlan.Existence of negative convex solutions for a discrete mixed boundary value problem with p-Laplacian operator[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):171-176.
赵亚丽,陈天兰.带p-Laplace算子的离散混合边值问题负凸解的存在性[J].中山大学学报(自然科学版),2023,62(06):171-176. DOI： 10.13471/j.cnki.acta.snus.2021A077.
ZHAO Yali,CHEN Tianlan.Existence of negative convex solutions for a discrete mixed boundary value problem with p-Laplacian operator[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(06):171-176. DOI： 10.13471/j.cnki.acta.snus.2021A077.
![PDF下载](/rc-pub/front/front-article/download/43168166/lowqualitypdf/带<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mi mathvariant="bold-italic">p</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/4574512A-E56C-46ca-B8E7-F759144E6721-M001.jpg"><?fx-imagestate width="4.23333359" height="6.85799980"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/4574512A-E56C-46ca-B8E7-F759144E6721-M001c.jpg"><?fx-imagestate width="4.23333359" height="6.85799980"?></graphic></alternatives></inline-formula>-Laplace算子的离散混合边值问题负凸解的存在性.pdf){kind=link}
摘要
运用锥上的不动点定理讨论带
<math id="M3"><mi>p</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097313&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097301&type=
1.77800000
2.96333337
-Laplace算子的离散混合边值问题
<math id="M4"><mo>△</mo><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mo>△</mo><mi>u</mi><mfenced separators="|"><mrow><mi>t</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>f</mi><mfenced separators="|"><mrow><mi>t</mi><mo>
</mo><mo>-</mo><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfenced><mo>
</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097323&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097321&type=
45.46599960
4.57200003
<math id="M5"><mi>t</mi><mo>∈</mo><msub><mrow><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>
</mo><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow><mrow><mi mathvariant="double-struck">Z</mi></mrow></msub><mo>
</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097329&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097334&type=
19.64266586
3.80999994
<math id="M6"><mo>△</mo><mi>u</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced><mo>=</mo><mn mathvariant="normal">0</mn><mo>
</mo><mi>u</mi><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><mn mathvariant="normal">0</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097350&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097337&type=
26.83933067
3.21733332
负凸解的存在性，其中
<math id="M7"><msub><mrow><mi>φ</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mi>s</mi></mrow></mfenced><mo>=</mo><msup><mrow><mfenced open="|" close="|" separators="|"><mrow><mi>s</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>s</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097354&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097351&type=
19.04999924
4.14866638
，
<math id="M8"><mi>p</mi><mo>></mo><mn mathvariant="normal">1</mn><mo>
</mo><mtext> </mtext><mi>f</mi><mtext> </mtext><mo>:</mo><mtext> </mtext><msub><mrow><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>
</mo><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow><mrow><mi mathvariant="double-struck">Z</mi></mrow></msub><mo>×</mo><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>
</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo><mo>→</mo><mtext> </mtext></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097346&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097356&type=
46.56666946
3.80999994
<math id="M9"><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>
</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097366&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097364&type=
10.07533360
2.96333337
连续.
Abstract
By using the fixed point theorem in cones， the existence of negative convex solutions for a discrete mixed boundary value problem of
<math id="M10"><mi>p</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097372&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097369&type=
2.03200006
3.47133350
-Laplacian operator
<math id="M11"><mo>△</mo><mfenced open="[" close="]" separators="|"><mrow><msub><mrow><mi>φ</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mo>△</mo><mi>u</mi><mfenced separators="|"><mrow><mi>t</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow></mfenced></mrow></mfenced><mo>=</mo><mi>f</mi><mfenced separators="|"><mrow><mi>t</mi><mo>
</mo><mo>-</mo><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mfenced><mo>
</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097385&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097382&type=
46.65133286
4.57200003
<math id="M12"><mo> </mo><mi>t</mi><mo>∈</mo><msub><mrow><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>
</mo><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow><mrow><mi mathvariant="double-struck">Z</mi></mrow></msub><mo>
</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097397&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097393&type=
24.89200020
4.48733330
<math id="M13"><mo>△</mo><mi>u</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn></mrow></mfenced><mo>=</mo><mn mathvariant="normal">0</mn><mo>
</mo><mo> </mo><mi>u</mi><mfenced separators="|"><mrow><mi>T</mi></mrow></mfenced><mo>=</mo><mn mathvariant="normal">0</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097391&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097388&type=
33.35866928
3.80999994
is studied， where
<math id="M14"><mtext> </mtext><msub><mrow><mi>φ</mi></mrow><mrow><mi>p</mi></mrow></msub><mfenced separators="|"><mrow><mi>s</mi></mrow></mfenced><mo>=</mo><msup><mrow><mfenced open="|" close="|" separators="|"><mrow><mi>s</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>-</mo><mn mathvariant="normal">2</mn></mrow></msup><mi>s</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097407&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097409&type=
22.77533340
4.74133301
，
<math id="M15"><mtext> </mtext><mi>p</mi><mo>></mo><mn mathvariant="normal">1</mn></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097416&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097423&type=
8.80533314
3.47133350
，
<math id="M16"><mtext> </mtext><mi>f</mi><mtext> </mtext><mo>:</mo><mtext> </mtext><msub><mrow><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">2</mn><mo>
</mo><mi>T</mi><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfenced></mrow><mrow><mi mathvariant="double-struck">Z</mi></mrow></msub><mo>×</mo><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>
</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097420&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097419&type=
37.84600067
4.48733330
<math id="M17"><mo>→</mo><mo stretchy="false">[</mo><mn mathvariant="normal">0</mn><mo>
</mo><mo>+</mo><mi mathvariant="normal">∞</mi><mo stretchy="false">)</mo></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097433&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097430&type=
16.76399994
3.47133350
is continuous.
关键词
<math id="M18"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097436&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097422&type=1.778000002.96333337-Laplace算子离散混合边值问题负凸解不动点定理锥
Keywords
<math id="M19"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097441&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51097453&type=2.032000063.47133350-Laplacian operatordiscrete mixed boundary value problemnegative convex solutionsfixed point theoremcone
references
CHU J F， JIANG D Q， 2005. Eigenvalues and discrete boundary value problems for the one-dimensional <math id="M243"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-Laplacian［J］. J Math Anal Appl， 305（2）： 452-465.
COSSIO J， HERRÓN S， VÉLEZ C， 2011. Infinitely many radial solutions for a <math id="M244"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-Laplacian problem <math id="M245"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-superlinear at the origin［J］. J Math Anal Appl， 376（2）： 741-749.
CHEN T， MA R， 2019a. Three positive solutions of <math id="M246"><mi>N</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098961&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098957&type=2.286000012.28600001-dimensional <math id="M247"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-Laplacian with indefinite weight［J］. Electron J Qual Theory Differ Equ， （19）： 1-14.
CHEN T， MA R， LIANG Y， 2019b. Multiple positive solutions of second-order nonlinear difference equations with discrete singular <math id="M248"><mi>ϕ</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098967&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098965&type=2.032000062.87866688-Laplacian［J］. J Differ Equ Appl， 25（1）： 38-55.
ERCOLE G， ZUMPANO A， 2001. Existence of positive radial solutions for the <math id="M249"><mi>n</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098985&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098969&type=1.608666662.28600001-dimensional <math id="M250"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-Laplacian［J］. Nonlinear Anal Theory Methods Appl， 44（3）： 355-360.
HE T， CHEN W， 2008. Periodic solutions of second order discrete convex systems involving the <math id="M251"><mi>p</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098977&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51098973&type=1.778000002.96333337-Laplacian［J］. Appl Math Comput， 206（1）： 124-132.
INFANTE G， WEBB J R L， 2002. Nonzero solutions of Hammerstein integral equations with discontinuous kernels［J］. J Math Anal Appl， 272（1）： 30-42.
KRASNOSELʹSKIĬ M A， 1964. Positive solutions of operator equations［M］. Groningen： Noordhoff.
LAN K Q， 2001. Multiple positive solutions of semilinear differential equations with singularities［J］. J London Math Soc， 63（3）： 690-704.
LIANG Z， YANG Y， 2019. Radial convex solutions of a singular Dirichlet problem with the mean curvature operator in Minkowski space［J］. Acta Math Sci， 39（2）： 395-402.
TIAN Y， GE W， 2008. The existence of solutions for a second-order discrete Neumann problem with a p-Laplacian［J］. J Appl Math Comput， 26（1/2）： 333-340.
TIAN Y， GE W， 2012. Two solutions for a discrete problem with a p-Laplacian［J］. J Appl Math Comput， 38（1/2）： 353-365.
0
浏览量
14
下载量
0
CSCD
- 网络PDF下载
- Meta-XML下载
- BibTeX下载
- Endnote下载
- RefMan 下载
- NoteExpress下载
- NoteFirst下载
关联资源
相关文章
相关作者
相关机构
- 地址：广州市海珠区新港西路135号 中山大学南校园东北区311栋 邮编：510275
- 联系电话：020-84112585，84113223 Email：xuebaozr@mail.sysu.edu.cn
- 技术支持由北京北大方正电子有限公司提供 京ICP备09064830号-19
京公网安备11010802024621 - 本系统建议在Chrome、 IE9+ 以上版本浏览器阅读本站内容，360浏览器请切换至极速模式
- Cookies帮助我们提供服务并提供个性化体验。使用本网站，即表示您同意我们使用Cookies
