非线性二阶Neumann边值问题的Ambrosetti-Prodi型结果

doi:10.6040/j.issn.1671-9352.0.2014.326

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (03): 62-66.doi: 10.6040/j.issn.1671-9352.0.2014.326

非线性二阶Neumann边值问题的Ambrosetti-Prodi型结果

马陆一

西北师范大学数学与统计学院, 甘肃兰州 730070

收稿日期:2014-07-15 修回日期:2014-11-07 出版日期:2015-03-20 发布日期:2015-03-13
作者简介:马陆一(1991- ), 男, 硕士研究生, 研究方向为常微分方程边值问题.E-mail:maly0318@126.com
基金资助:
国家自然科学基金资助项目(11361054);甘肃省自然科学基金资助项目(1208RJZA258)

The Ambrosetti-Prodi type results of the nonlinear second-order Neumann boundary value problem

MA Lu-yi

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China

Received:2014-07-15 Revised:2014-11-07 Online:2015-03-20 Published:2015-03-13

摘要/Abstract

摘要： 研究了二阶Neumann边值问题

解的个数与参数s的关系, 其中f∈C([0,1]×R²,R), s∈R。运用上下解方法及拓扑度理论, 获得存在常数 s₁∈R, 当s<s₁时, 该问题没有解; s=s₁时, 该问题至少有一个解; s>s₁时, 该问题至少有两个解。

关键词: Ambrosetti-Prodi问题, 上下解方法, 拓扑度

Abstract: We study the relationship between s and the number of solutions of the second-order Neumann boundary value problem

where f∈C([0,1]×R²,R), s∈R is a parameter. By using the method of the upper and lower solutions and topological degree techniques, we obtain that the problem has no solution, at least one solution and at least two solutions, when s<s₁, s=s₁, s>s₁, respectively.

Key words: topological degree, upper and lower solutions, Ambrosetti-Prodi problem

中图分类号:

O175.8

马陆一. 非线性二阶Neumann边值问题的Ambrosetti-Prodi型结果[J]. 山东大学学报（理学版）, 2015, 50(03): 62-66.

MA Lu-yi. The Ambrosetti-Prodi type results of the nonlinear second-order Neumann boundary value problem[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 62-66.

参考文献

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非线性二阶Neumann边值问题的Ambrosetti-Prodi型结果

The Ambrosetti-Prodi type results of the nonlinear second-order Neumann boundary value problem

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