| 一类四阶边值问题的正解 |
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| 引用本文： | 任立顺. 一类四阶边值问题的正解[J]. 高校应用数学学报(英文版), 2003, 18(2): 138-142. DOI: 10.1007/s11766-003-0017-2 |
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| 作者姓名： | 任立顺 |
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| 作者单位： | Ren LishunDept. of Math.,Zhoukou Teachers College,Henan 466000,China. |
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| 摘 要： | § 1 IntroductionThe deformations of an elastic beam are described by a fourth-order two-pointbound-ary value problem[1 ] .The boundary conditions are given according to the controls at theends of the beam. For example,the nonlinear fourth order problemu(4) (x) =λa(x) f(u(x) ) ,u(0 ) =u′(0 ) =u′(1 ) =u (1 ) =0 (1 .1 ) λdescribes the deformations of an elastic beam whose one end fixed and the other slidingclamped.The existence of solutions of (1 .1 ) λhas been studied by Gupta[1 ] . But …
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| 收稿时间： | 2002-10-29 |
Positive solutions of a fourth order boundary value problem |
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| Ren Lishun. Positive solutions of a fourth order boundary value problem[J]. Applied Mathematics A Journal of Chinese Universities, 2003, 18(2): 138-142. DOI: 10.1007/s11766-003-0017-2 |
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| Authors: | Ren Lishun |
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| Affiliation: | Dept.of Math.,Zhoukou Teachers College, Henan 466000,China |
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| Abstract: | The existence of positive solutions of the nonlinear fourth order problem  is studied, where a:[0,1]→R may change sign, f(0)>0, λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem. |
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| Keywords: | fourth-order boundary value problem positive solution Leray-Schauder fixed point theorem. |
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