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《Journal of Wuyi University(Natural Science Edition)》 2005-01
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Solvability of a Fourth-Order Two-Point BVP under the Nonsymmetric Boundary Condition

YAO Qing-liu(Dept. of Applied Math., Nanjing Univ. of Finance and Economics, Nanjing 210046, China)  
The existence of a solution or a positive solution is considered for the nonlinear fourth-order two-point boundary value problem with all-order derivatives?u(4)(t) = f (t,u(t), u′(t), u′′(t), u′′′(t)), 0 ≤ t ≤1,??u′(0) = C, u′′(0) = B, u′′′(0) = A, ku(1) ? u′′′(1) = D where 0 k ≤ 6. The boundary condition of this problem is nonsymmetric. The mathematical models of the vibration of beams are given by fourth-order boundary value problems. The problems with all-order derivatives can describe more precisely the vibration of beams. By constructing a suitable Banach space and applying corresponding integral equation, two existence theorems are established. The main ingredient is Leray-Schauder fixed point theorem. This paper shows that the problem has at least one solution or positive solution provided the “height” of nonlinear term f is appropriate on some bounded subset of its domain.
【CateGory Index】: O175.8
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【References】
Chinese Journal Full-text Database 1 Hits
1 YAO Qing-liu(Dep.of Appl.Math.,Nanjing Univ.of Finance and Economics,Nanjing 210003,China);Solvability of Nonlinear Fourth-Order Beam Equations[J];Journal of Wuyi University(Natural Science Edition);2006-02
【Citations】
Chinese Journal Full-text Database 2 Hits
1 LI FUYI(Department of Mathematics, Shandong University, Jinan 250100);EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS OF SOME NONLINEAR EQUATIONS[J];Acta Mathematicae Applicatae Sinica;1997-04
2 LI YONGXIANG (Department of Mathematics, Northwest Normal University, Lanzhou 730070);EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR FOURTH-ORDER BOUNDARY VALUE PROBLEMS[J];Acta Mathematicae Applicatae Sinica;2003-01
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 WU Hong ping (Department of Mathematics, Northwest Normal University, Lanzhou 730070,China);The existence of positive solution of an elastic beam equation[J];Pure and Applied Mathematics;2001-04
2 ZHAO Hong(School of Mathematics,Changchun Normal University,Changchun 130032,China);Existence of solutions for fourth-order boundary value problems[J];Journal of Changchun University;2007-12
3 WAN Aying1,2,XU Xiaojie2,JIANG Daqing2(1Department of Mathematics,Hulunbeier College,Hailaer 021008,China;2Department of Mathematics,Northeast Normal University,Changchun 130024,China);Positive solutions to a singular nonlinear fourth order two point boundary value problem[J];Journal of Northeast Normal University (Natural Science Edition);2003-03
4 ZHU Xiao-jie~1,QIAO Xing-hao~2,ZHAO Yu-rong~1 (1.Dept of Mathematics,Mudanjiang Normal University,Mudanjiang,Heilongjiang157002,China;2.Dept of Fundamental Science,Tsinghua University,Beijing 100084,China);Positive solution to a nonlinear fourth-order periodic boundary value problem[J];Journal of Daqing Petroleum Institute;2006-03
5 CHEN Shun-qing (Department of Math,Daxian Teachers College,Dazhou Sichuan 635000,China);Existence ofPositive Solutions for a Class Fourth-order Operator Boundary Value Problems[J];Journal of Daxian Teachers College;2005-02
6 ZHANG Huan-huan(College of Mathematics and Information Science,Northwest Normal University,Lanzhou 730070,China);Existence and uniqueness of solutions for fourth-order two-point boundary value problems[J];Basic Sciences Journal of Textile Universities;2006-04
7 ZHANG Yan-hong, ZENG You-dong(College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China);The existence of positive solution for a four-order three-point boundary value problem[J];Journal of Fuzhou University(Natural Sciences Edtion);2005-01
8 ZHANG Yan-hong,LU·· Hui(College of Mathematics and Computer Science,Fuzhou University,Fuzhou,Fujian 350002,China);The existence of positive solution for a four-order three-point singular boundary value problem[J];Journal of Fuzhou University(Natural Science Edition);2006-03
9 WU Hong-ping(College of Mathematics and Information science, Northwest Normal University, Lanzhou 730070);Multiple Positive Solutions of Fourth Order Singular Nonlinear Eigenvalue Problem[J];Chinese Journal of Engineering Mathematics;2004-02
10 ZHANG Jian-guo1, ZHANG Fu-wei2, LIU Jin-shen2 (1- Faculty of Science, North China University of Technology, Beijing 100041; 2- Faculty of Science, Taiyuan University of Technology, Taiyuan 030024);The Existence and Multiplicity of Positive Solutions for a Class of Fourth Order Boundary Value Problem[J];Chinese Journal of Engineering Mathematics;2005-05
【Co-references】
Chinese Journal Full-text Database 3 Hits
1 YAO Qing-liu (Department of Applied Math., Nanjing University of Finance and Economics,Nanjing 210046, Jiangsu, China);Existence and multiplicity of positive solutions to a class of elastic beam equations[J];Journal of Shandong University(Natural Science);2004-05
2 YAO Qing-liu~1,REN Li-shun~2 (1.Department of Applied Mathematics,Nanjing University of Finance and Economics, Nanjing 210046,China; 2.Depertment of Mathematics,Zhoukou Teachers College,Zhoukou 466000,China);Solution and Positive Solution to a Class of Nonlinear Fourth-order Boundary Value Problems[J];Journal of Xiamen University(Natural Science);2004-06
3 YAO QINGLIU (Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003);EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF NONLINEAR ELASTIC BEAM EQUATIONS WITH BOUNDED-BELOW NONLINEARITY[J];Acta Mathematicae Applicatae Sinica;2004-01
【Secondary References】
Chinese Journal Full-text Database 1 Hits
1 YANG Jing-bao1,WEI Zhong-li2(1.Department of Science,Bozhou Teachers College,Mengcheng 233500;2.School of Sciences,Shandong Jianzhu University,Jinan 250101,China);Solvability of One-dimensional p-Laplacian Operator Equation with First Derivative[J];Journal of Anqing Teachers College(Natural Science Edition);2008-01
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