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Existence and multiplicity of solutions for a class of fourth-order two-point boundary value problems with parameters
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 59, Issue 6, Pages: 163-169(2020)
- 作者机构：
兰州交通大学数理学院，甘肃 兰州 730070
- 作者简介：
- 基金信息：
DOI：10.13471/j.cnki.acta.snus.2019.10.10.2019A077
CLC： O175.8Published：25 November 2020，
Received：10 October 2019，
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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
9.82133293
这里参数
<math id="M2"><mi>α</mi><mo>
</mo><mi>β</mi><mo>∈</mo><mi mathvariant="normal">R</mi></math>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490482&type=
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11.00666714
2.87866688
且
<math id="M3"><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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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490484&type=
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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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490495&type=
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>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490518&type=
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16.51000023
7.02733326
。在非线性项
<math id="M6"><mi>f</mi></math>
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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
<math id="M7"><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>
</mo><mi>u</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>
</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>t</mi><mo>∈</mo><mo stretchy="false">(</mo><mn mathvariant="normal">0
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>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490511&type=
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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>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490548&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490531&type=
12.53066635
7.95866680
，
<math id="M10"><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>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490538&type=
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>
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490542&type=
https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49490555&type=
19.04999924
7.95866680
.Under certain conditions of the nonlinear term
<math id="M12"><mi>f</mi></math>
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1.10066664
3.47133350
， 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
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