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奇异二阶方程组两个正解的存在性 被引量：1

Existence of Twin Positive Solutions for Singular Second Order Differential Systems
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摘要 用Leray-Schauder非线性抉择和更一般的锥不动点定理研究奇异二阶方程组边值问题两个正解的存在性,给出了正解存在的充分条件,并举例说明了所得结果。 We investigated the existence of two positive solutions to singular boundary value problems using Leray-Schauder alternative theorem and other fixed point theorems in cones,obtained its sufficient conditions and gave an example to explain our results.
作者 千美华 从福仲 许晓婕
机构地区 吉林省教育学院 空军航空大学基础部 吉林大学数学研究所 中国石油大学(华东)应用数学系
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2010年第5期755-760,共6页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10871203)
关键词 两点边值问题 两个正解 LERAY-SCHAUDER非线性抉择 锥不动点定理 方程组 two-point boundary problems twin positive solutions Leray-Schauder alternative fixed point theorems differential systems
分类号 O175.08 [理学—基础数学]
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参考文献2

二级参考文献12

  • 1Agarwal R P, O'Regan D. Nonlinear Superlinear Singular and Nonsingular Second Order Boundary Value Problems [J]. Journal of Differential Equations, 1998, 143: 60-95.
  • 2Agarwal R P, O'Regan D. Twin Solutions to Singular Dirichlet Problems [J]. J Math Anal Appl, 1999, 240: 433-445.
  • 3Agarwal R P, O'Regan D. Twin Solutions to Singular Boundary Value Problems [J]. Proc Amer Math Soc, 2000, 128(7): 2085-2094.
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  • 5JIANG Da-qing. Multiple Positive Solutions to Singular Boundary Value Problems for Superlinear Higher-order ODEs [J]. Computers and Mathematics with Applications, 2000, 40: 249-259.
  • 6XU Xiao-jie, JIANG Da-qing. Twin Positive Solutions to Singular Boundary Value Problems of Second Order Differential Systems [J]. Indian Journal of Pure and Applied Mathematics, 2003, 34: 85-99.
  • 7JIANG Da-qing. On the Existene of Positive Solutions to Second Order Periodic BVPs [J]. Acta Mathematica Scientia, 1998, 18: 31-35.
  • 8WANG Jun-yu, JIANG Da-qing. A Singular Nonlinear Second Order Periodic Boundary Value Problem [J]. Tohoku Math J, 1998, 50: 203-210.
  • 9Krasnosel'skii M A. Positive Solutions of Operator Equations [M]. Netherland: Noordhoff Groningen, 1964.
  • 10蒋达清.ON THE EXISTENCE OF POSITIVE SOLUTIONS TO SECOND ORDER PERIODIC BVPS[J].Acta Mathematica Scientia,1998,18(S1):31-35. 被引量：28

共引文献10

同被引文献14

  • 1Agarwal R P, O' Regan D. Existence Theory for Single and Multiple Solutions to Singular Positone Boundary Value Problems [J]. J Differential Equations, 2001, 175(2) : 393-414.
  • 2JIANG Da-qing, GAO Wen-jie. Upper and Lower Solution Method and a Singular Boundary Value Problem for the One-Dimension p-Laplacian [ J ]. J Math Anal Appl, 2000, 252 (2) : 631-648.
  • 3JIANG Da-qing, LIU Hui-zhao. On the Existence of Nonnegative Radial Solutions for p-Laplacian Elliptic Systems [ J ]. Ann Polon Math, 1999, 71(1) : 19-29.
  • 4JIANG Da-qing. Upper and Lower Solutions Method and a Superlinear Singular Boundary Value Problem for the One-Dimensional p-Laplacian [ J]. Computers and Mathematics with Applications, 2001, 42 (6/7) : 927-940.
  • 5Manasevich R, Zanolin F. Time-Mappings and Multiplicity of Solutions for the One-Dimensional p-Laplacian [ J ]. Nonlinear Analysis : Theory, Methods and Applications, 1993, 21 (4) : 269-291.
  • 6WANG Jun-yu, GAO Wen-jie. A Singular Boundary Value Problem for the One-Dimensional p-Laplacian [ J ]. J Math Anal Appl, 1996, 201(3) : $51-866.
  • 7KONG Ling-bin, WANG Jun-yu. Muhiple Positive Solutions for the One-Dimensional p-Laplacian [ J ]. Nonlinear Anal : Theory, Methods and Applications, 2000, 42 (8) : 1327-1333.
  • 8ZHANG Mei-rong. Nonuniform Nonresonance at the First Eigenvalue of the p-Laplacian [ J ], Nonlinear Anal : Theory, Methods and Applications, 1997, 29(1) : 41-51.
  • 9O' Regan D. Existence Theorey for Nonlinear Ordinary Differential Equations [ M]. Dordrecht: Kuwer Academic, 1997.
  • 10HU Wei-min, JIANG Da-qing, LUO Ge-xin, Theory for Single and Multiple Solution to Singular Discrete Boundary Value Problems for Second-Order Differential Systems [ J]. Dynamic Systems and Applications, 2008, 17: 221-234.

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吉林大学学报（理学版）
2010年 第5期

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