一类带参数的四阶两点边值问题的多解性
Existence and multiplicity of solutions for a class of fourth-order two-point boundary value problems with parameters
- 中山大学学报(自然科学版) 2020年59卷第6期 页码：163-169
- 作者机构：
兰州交通大学数理学院，甘肃 兰州 730070
- 作者简介：
张建梅(1991年生)，女；研究方向：非线性边值问题；E-mail:19893171158@163.com
李杰梅(1981年生)，女；研究方向：非线性边值问题；E-mail: lijiemei81@126.com
- 基金信息：国家自然科学基金(11801243);国家自然科学基金(61863022);甘肃省自然科学基金(1308RJZA113);甘肃省高校基本科研业务费基金(2120840);甘肃省高等学校创新能力提升项目(2019B-054)
DOI：10.13471/j.cnki.acta.snus.2019.10.10.2019A077
中图分类号： O175.8纸质出版日期：2020-11-25，
收稿日期：2019-10-10，
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张建梅,李杰梅.一类带参数的四阶两点边值问题的多解性[J].中山大学学报(自然科学版),2020,59(06):163-169.
ZHANG Jianmei,LI Jiemei.Existence and multiplicity of solutions for a class of fourth-order two-point boundary value problems with parameters[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(06):163-169.
张建梅,李杰梅.一类带参数的四阶两点边值问题的多解性[J].中山大学学报(自然科学版),2020,59(06):163-169. DOI： 10.13471/j.cnki.acta.snus.2019.10.10.2019A077.
ZHANG Jianmei,LI Jiemei.Existence and multiplicity of solutions for a class of fourth-order two-point boundary value problems with parameters[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2020,59(06):163-169. DOI： 10.13471/j.cnki.acta.snus.2019.10.10.2019A077.
摘要
研究一类带参数的四阶两点边值问题
<math id="M1"><mfenced open="{" close="" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><msup><mrow><mi>u</mi></mrow><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">4</mn><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo><mi>β</mi><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>-</mo><mi>α</mi><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>t</mi><mo>
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73.32133484
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这里参数
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</mo><mi>β</mi><mo>∈</mo><mi mathvariant="normal">R</mi></math>
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11.00666714
2.87866688
且
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10.83733368
7.02733326
，
<math id="M4"><mi>β</mi><mo><</mo><mn mathvariant="normal">2</mn><msup><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></math>
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10.24466705
3.13266659
，
<math id="M5"><mfrac><mrow><mi>α</mi></mrow><mrow><msup><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>β</mi></mrow><mrow><msup><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo><</mo><mn mathvariant="normal">1</mn></math>
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16.51000023
7.02733326
。在非线性项
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0.93133330
2.96333337
满足一定的条件下，运用Leggett-Williams不动点定理，获得所讨论问题至少三个非负解的存在性结果。
Abstract
A class of fourth-order two-point boundary value problems with parameters
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</mo><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>
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1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mtd></mtr></mtable></mrow></mfenced></math>
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73.32133484
9.82133293
are studied， where the parameters
<math id="M8"><mi>α</mi><mo>
</mo><mi>β</mi><mo>∈</mo><mi mathvariant="normal">R</mi></math>
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12.78466702
3.38666677
and
<math id="M9"><mi>α</mi><mo>≥</mo><mo>-</mo><mfrac><mrow><msup><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow><mrow><mn mathvariant="normal">4</mn></mrow></mfrac></math>
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12.53066635
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，
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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490551&type=
11.76866722
3.64066648
，
<math id="M11"><mfrac><mrow><mi>α</mi></mrow><mrow><msup><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>β</mi></mrow><mrow><msup><mrow><mi mathvariant="normal">π</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo><</mo><mn mathvariant="normal">1</mn></math>
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19.04999924
7.95866680
.Under certain conditions of the nonlinear term
<math id="M12"><mi>f</mi></math>
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， the existence of at least three non-negative solutions for the discussed problem are obtained by using fixed point results of Leggett-Williams type.
关键词
四阶多解性Leggett-Williams不动点定理
Keywords
fourth-ordermultiple positive solutionsLeggett-Williams fixed point theorem
references
LI Y X. Positive solutions of fourth-order boundary value problems with two parameters ［J］.Math Anal Appl， 2003，281： 477-484.
CUI Y Q. Multiple solutions to fourth-order boundary value problems ［J］. Appl Math Comput，2009，57： 643-649.
HE T S， SU Y L. On discrete fourth-order boundary value problems with three parameters ［J］.Appl Math Comput， 2010， 233（10）： 2506-2520.
MA R Y， XU L. Existience of positive solutions of a nonlinear fourth-order boundary value problem ［J］. Appl Math Lett， 2010，23： 537-543.
岳蔓，韩晓玲.带参数的四阶两点边值问题正解的存在性［J］.四川师范大学学报（自然科学版），2015，38（3）：333-336.
YUE M，HAN X L.Existence of solutions for fourth-order two-point boundary value problems with parameters ［J］.Journal of Sichuan Normal University：Natueal Science，2015，38（3）：333-336.
CABADA A， SAAVEDRA L. Existence of solutions for <math id="M252"><mi>n</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49492059&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49492057&type=1.608666662.28600001th nonlinear differential boundary value problems by means of fixed point theorems ［J］.Nonlinear Anal Real World Appl，2018，42： 180-206.
CABADA A， PRECUP R， SAAVEDRA L， et al.Multiple solutions to a fourth-order boundary value problem ［J］. Differential Equations，2016，254： 1-18.
AVERY R I，ELOE P，HENDERSON J. A Leggett-Williams type theorem applied to a fourth order problem ［J］. Commun Appl Anal，2012，16（4）： 578-588.
GUPTA C P. Existence and uniqueness theorems for a bending of an elastic beam equation ［J］.Appl Anal，1988，26： 289-304.
GUPTA C P. Existence and uniqueness results for the bending of an elastic beam equation at resonance ［J］. Math Anal Appl，1988，135： 208-225.
林壮鹏，徐远通，郭志明.一类非线性算子的不动点理论及其应用［J］.中山大学学报（自然科学版），2000，39（6）：26-29.
LIN Z P，XU Y T，GUO Z M.Fixed point theorems of a class of nonlinear operators and their applications ［J］.Acta Scientiarum Naturalium Universitatis Sunyatseni， 2000，39（6）： 26-29.
成立花.Banach空间混合型泛函方程的稳定性问题［J］.中山大学学报（自然科学版），2017，56（6）： 68-71.
CHENG L H.Stability of a mixed type functional equation in Banach spaces ［J］.Acta Scientiarum Naturalium Universitatis Sunyatseni， 2017，56（6）： 68-71.
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