| 具共振条件下的一类三阶非局部边值问题的可解性 |
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| 引用本文： | 杜增吉,林晓洁,葛渭高. 具共振条件下的一类三阶非局部边值问题的可解性[J]. 数学学报, 2006, 49(1): 87-94. DOI: cnki:ISSN:0583-1431.0.2006-01-015 |
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| 作者姓名： | 杜增吉 林晓洁 葛渭高 |
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| 作者单位： | 北京理工大学数学系,徐州师范大学数学系,北京理工大学数学系 北京 100081,徐州 21116,北京 100081 |
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| 基金项目： | 国家自然科学基金资助项目（40301037）;致谢 作者衷心感谢审稿人提出的宝贵修改意见. |
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| 摘 要： | 本文考虑一类三阶非局部边值问题x”’(t)=f(t,x(t),x'(t),x”(t)),t∈(0,1), x(0)=0,x'(0)=0,x'(1)=(?) x'(s)dg(s),其中f:[0,1]×R3→R是一个连续函数, g:[0,1]→[0,∞)是一个非减的函数,且满足g(0)=0．在g满足共振条件g(1)=1 的情况下,通过应用重合度理论,得到了该问题解的存在性结果．
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| 关 键 词： | 非局部边值问题 共振 重合度理论 |
| 文章编号： | 0583-1431（2006）01-0087-08 |
| 收稿时间： | 2003-12-29 |
| 修稿时间： | 2003-12-292004-11-18 |
Solvability of a Third Order Nonlocal Boundary Value Problem at Resonance |
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| Zeng Ji DU. Solvability of a Third Order Nonlocal Boundary Value Problem at Resonance[J]. Acta Mathematica Sinica, 2006, 49(1): 87-94. DOI: cnki:ISSN:0583-1431.0.2006-01-015 |
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| Authors: | Zeng Ji DU |
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| Affiliation: | Zeng Ji DU Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China Xiao Jie LIN Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, P. R. China Wei Gao GE Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | In this paper, we consider a third order nonlocal boundary value problem x'"(t) = f(t,x(t),x'(t),x"(t)), t ∈ (0,1), x(0) = 0, x"(0) = 0, z'(1) =(?)x'(s)dg(s), where f : [0,1] x R3 →R is a continuous function, g : [0,1]→[0,∞) is a nonde-creasing function with g(0) = 0. Under the resonance condition g(1) = 1, an existence result is given by using the coincidence degree theory. |
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| Keywords: | nonlocal boundary value problem resonance coincidence degree theory |
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