| 一类二阶微分议程边值问题三解的存在性 |
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| 引用本文： | 刘斌. 一类二阶微分议程边值问题三解的存在性[J]. 高校应用数学学报(英文版), 2002, 17(2): 135-144. DOI: 10.1007/s11766-002-0037-3 |
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| 作者姓名： | 刘斌 |
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| 作者单位： | Liu BinDept.ofMath.,HuazhongUniv.ofScienceandTechnology,Wuhan430074,China.CollegeofMath.andStatist.,WuhanUniv.,Wuhan430072,China |
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| 基金项目： | SupportedbythePostdoctorScienceFoundationofChina(200114) |
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| 摘 要： | § 1 IntroductionWe are interested in the existence ofthree-solutions ofthe following second-order dif-ferential equations with nonlinear boundary value conditionsx″=f( t,x,x′) , t∈ [a,b] ,( 1 .1 )g1 ( x( a) ,x′( a) ) =0 , g2 ( x( b) ,x′( b) ) =0 ,( 1 .2 )where f:[a,b]×R1 ×R1 →R1 ,gi:R1 ×R1 →R1 ( i=1 ,2 ) are continuous functions.The study ofthe existence of three-solutions ofboundary value prolems forsecond or-der differential equations was initiated by Amann[1 ] .In[1 …
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| 关 键 词： | 二阶微分方程 边值问题 周期解 存在性 |
Existence of three-solutions for second-order differential equations with nonlinear boundary value conditions |
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| Liu Bin. Existence of three-solutions for second-order differential equations with nonlinear boundary value conditions[J]. Applied Mathematics A Journal of Chinese Universities, 2002, 17(2): 135-144. DOI: 10.1007/s11766-002-0037-3 |
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| Authors: | Liu Bin |
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| Affiliation: | (1) Dept. of Math., Huazhong Univ. of Science and Technology, 430074 Wuhan, China;(2) College of Math. and Statist., Wuhan Univ., 430072 Wuhan, China |
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| Abstract: | The paper deals with the existence of three-solutions for the second-order differential equations with nonlinear boundary value conditions where f:[a,b] × R 1 × R 1 → R 1, g i :R 1 × R 1 → R 1 (i=1,2) are continuous functions. The methods employed are the coincidence degree theory. As an application, the sufficient conditions under which there are arbitrary odd solutions for the BVP are obtained. Supported by the Postdoctor Science Foundation of China (200114). |
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| Keywords: | coincidence degree three- solutions theorem nonlinear boundary value conditions |
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![$$begin{gathered} x' = f(t,x,x'), t in left[ {a,b} right], hfill g_1 (x(a),x'(a)) = 0, g_2 (x(b), x'(b)) = 0, hfill end{gathered} $$](/content/564826425h3r5621/11766_2002_Article_37_TeX2GIFE1.gif)