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《Acta Analysis Functionalis Applicata》 2008-01
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On Positive Solutions of Singular Fourth-order Sturm-Liouville Boundary value Problem

WANG Rui1,2, QI Shi-shuo21. Department of Information and Computational Science, Henan Agricultural University,Zhengzhou 450002, China2. Department of Mathematics, Zhengzhou University, Zhengzhou, 450052, China  
We established a conclusion of the existence of positive solutions for the fourth-order boundary value problem {u(4)(t)-λh(t)f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0,αu″(0)-βu′″(0)=0, γu″(1)+δu′″(1)=0,where α,β,γ,δ≥0,α+β0,δ+γ0,ρ=αγ+γβ+δα0,λ is a positive parameter, h(t)∈C(0,1) and f∈C((0,1)×(0,+∞)). The main approaches for our research are the fixed point index theorem and the approximation theorem of completely continuous operator.
【Fund】: China Scholarship Council-henan Programme;; The Foundation for Key Teachers ofHenan Province
【CateGory Index】: O175.8
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Chinese Journal Full-text Database 1 Hits
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Chinese Journal Full-text Database 10 Hits
1 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
2 DU Xin-sheng(Department of Mathematics, Qufu Normal University, Qufu 273165);Positve Solution to Four Order Singular Boundary Value Problems[J];Chinese Journal of Engineering Mathematics;2003-06
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7 Chen Xiangping(Department of Mathematics,Jining University,Shandong,Jining,273155);Existence of Positive Solution to Fourth-Order Singular Differential Equations[J];Journal of Jining University;2008-06
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9 ZHAO Xiao-Hua1,LI Ling-Xiao2 (1.Department of Mathematics,Zhengzhou University,Zhengzhou 450052,China;2.Science College,Henan University of Science & Technology,Luoyang 471003,China);Research on Nonlinear Eigenvalue Problem of A Four Order Ordinary Differential Operater[J];Journal of Henan University of Science & Technology(Natural Science);2007-04
10 Zhang Ruojun (Department of Mathematics, Ocean University of Qingdao, Qingdao 266071, China);A Note on the Existence of Multiple Positive Solutionsof Fourth Order Singular Boundary Value Problems[J];Journal of Ocean University of Qingdao;2002-05
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