| 一类带参数四阶边值问题正解的存在性 |
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| 引用本文： | 杨丽娟. 一类带参数四阶边值问题正解的存在性[J]. 山东大学学报(理学版), 2021, 56(9): 35-41. DOI: 10.6040/j.issn.1671-9352.0.2020.457 |
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| 作者姓名： | 杨丽娟 |
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| 作者单位： | 西北师范大学数学与统计学院,甘肃 兰州730070 |
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| 基金项目： | 国家自然科学基金资助项目(11671322) |
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| 摘 要： | 研究了带参数四阶常微分方程(ordinary differential equation,ODE)边值问题({u?(t)+au?(t)+bu″(t)+cu′(t)+du(t)=rf(t,u(t),u″(t)),0
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| 关 键 词： | 四阶ODE 正解 分歧理论 Krein-Rutman定理 |
Existence of positive solutions for a class of fourth-order boundary value problems with parameter |
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| YANG Li-juan. Existence of positive solutions for a class of fourth-order boundary value problems with parameter[J]. Journal of Shandong University, 2021, 56(9): 35-41. DOI: 10.6040/j.issn.1671-9352.0.2020.457 |
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| Authors: | YANG Li-juan |
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| Affiliation: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China |
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| Abstract: | This article studies the boundary value problems of fourth-order ordinary differential equations with parameter{u'(t)+au(t)+bu″(t)+cu'(t)+du(t)=rf(t,u(t),u″(t)), 01,u(0)=u(1)=u″(0)=u″(1)=0,where r is a positive parameter, a,b,c,d are constant coefficients, and the nonlinearity f: ［0,1］×［0,∞)×(-∞,0］→［0,∞) is a continuous function. When r is in a cetain range of values, the existence of positive solutions are obtained by using global bifurcation theorem. |
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| Keywords: | fourth-order ODE positive solution bifurcation theorem Krein-Rutman theorem |
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