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二阶常微分方程组积分边值问题的正解 被引量：2

POSITIVE SOLUTIONS FOR A SYSTEM OF SECOND-ORDER ORDINARY DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS
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摘要 在借助于非负矩阵获得正解的先验估计的基础上,用不动点指数理论研究二阶非线性常微分方程组积分边值问题正解和多重正解的存在性. Based on a priori estimates achieved by utilizing nonnegative matrices, and by using the fixed point index theory, the existence and multiplicity of positive solutions for a system of nonlinear second-order ordinary differential equations with integral boundary conditions are satisfied.
作者 叶盼盼 杨志林
机构地区 青岛理工大学理学院
出处 《系统科学与数学》 CSCD 北大核心 2011年第8期992-999,共8页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(10971179)资助课题
关键词 积分边值问题 常微分方程组 不动点指数 正解. Integral boundary value problem, system of ordinary differential equations,fixed point index, positive solution.
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献7

  • 1杨志林,孙经先.非线性二阶常微分方程组边值问题的正解[J].数学学报（中文版）,2004,47(1):111-118. 被引量：44
  • 2Cheng X Y. Existence of positive solutions for a class of second-order ordinary differential systems. Nonlinear Analysis, 2008, 69: 3042-3049.
  • 3Yang Z L. Positive solutions to a system of second-order nonlocal boundary value problems. Non- linear Anal., 2005, 62: 1251-1265.
  • 4Liu B M, Liu L S, and Wu Y H. Positive solutions for singular systems of three-point boundary value problems. Computers and Mathematics with Applications, 2007, 53: 1429-1438.
  • 5Infante G and Pietramala P, Existence and multiplicity of nonnegative solutions for systems of perturbed Hammerstein integral equations. Nonlinear Analysis, 2009, 71: 1301-1310.
  • 6杨志林,孙经先.非线性算子的渐近歧点[J].系统科学与数学,2000,20(1):47-54. 被引量：12
  • 7[7]孙经先.非线性泛函分析及其应用[M].北京:科学出版社,2007.

二级参考文献6

共引文献54

同被引文献20

  • 1邹玉梅,崔玉军.二阶微分方程组的耦合积分边值问题[J].应用泛函分析学报,2013,15(2):125-130. 被引量：2
  • 2[7]孙经先.非线性泛函分析及其应用[M].北京:科学出版社,2007.
  • 3Boucherif A. Second-order boundary value problems with integral boundary conditions[J]. Nonlinear Anal- ysis, 2009, 70(1): 364-371.
  • 4Feng M, Ji D, Ge W. Positive Solutions for a class of boundary value problem with integral boundary conditions in Banach spaces[J]. Journal of Computational and Applied Mathematics, 2008, 222(2): 351- 363.
  • 5Kang P, Wei Z, Xu J. Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces[J]. Applied Mathematics and Computation 2008, 206(1): 245-256.
  • 6Li Y, Li F. Sign-changing solutions for second order integral boundary value problems[J]. Nonlinear Analysis, 2008, 69(4): 1179-1187.
  • 7Yang Z. Existence and uniqueness of positive solutions for an integral boundary value problem[J]. Non- linear Analysis, 2008, 69(11): 3910-3918.
  • 8Yang Z. Existence of nontrivial solutions for a nonlinear Sturm-Liouville problem with integral boundary conditions[J]. Nonlinear Analysis, 2008, 68(1): 216-225.
  • 9Zhang X, Sun J. On multiple sign-changing solutions for some second-order integral boundary value problems[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2010, 44: 1-15.
  • 10Boucherif A. Second-order boundary value problems with integral boundary conditions. Nonliear Analalysis, 2009, 70: 364-371.

引证文献2

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系统科学与数学
2011年 第8期

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