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一类超线性奇异半正方程组正解的存在性 被引量：1

Existence of Positive Solution for A Superlinear Semipositone Singular Differential System
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摘要 通过把所研究的问题转化为相应的全连续算子的不动点问题,利用范数形式的锥拉伸与锥压缩不动点定理得出了一类二阶超线性奇异半正方程组在m点边值条件下正解的存在性结果,并给出了一个例子作为对所获结果的应用. By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for m-point boundary value problem of second-order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and ex pansion in norm type. One example is presented to illustrate the application of the obtained results.
作者 王峰 张国伟
机构地区 盐城机电高等职业技术学院 东北大学数学系
出处 《淮阴师范学院学报（自然科学版）》 CAS 2009年第2期96-102,107,共8页 Journal of Huaiyin Teachers College;Natural Science Edition
关键词 超线性奇异半正方程组 正解 不动点定理 锥 superlinear singular semipositone differential system positive solution fixed point theorem cone
分类号 O175.14 [理学—基础数学] O175.8 [理学—基础数学]
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参考文献10

  • 1Guo D J, Lakshmikantham V. Nonlinear problems in abstract cones [M]. San Diego: Academic Press, 1998,24- 56.
  • 2Anuradha V, Hai D, Shivaji R. Existence results for superlinear semipositone BVP's [J]. Pro Amer Math Soc, 1996, 124:747 - 763.
  • 3Agarwal R P, O' Regan D. A note on existence of nonnegative solutions to singular semipositone problems / J ]. Nonlinear Anal, 1999, 36: 615-622.
  • 4Xu X. Positive solutions for singular semi-positone boundary value problems [J], J Math Anal Appl, 2002,273:480- 491.
  • 5Zhang X G, Liu L S. Positive solutions of superlinear semipositone singular Dirichlet boundary value problems [ J]. J Math Anal Appl, 2006, 316: 525-537.
  • 6Fink A M, Gatica J A. Positive solutions of second order systems of boundary value problems [J]. J Math Anal Appl, 1993, 180: 93- 108.
  • 7Agarwal R P, O'Regan D. A coupled system of boundary value problems [J]. Appl Anal, 1998, 69:381 - 385.
  • 8Xu X. Positive solutions for singular semipositone three-point systems [J]. Nonlinear Anal, 2007, 66:791 -805.
  • 9Liu L S, Zhang X G, Wu Y H. On existence of positive solutions of a two-point boundary prob-lem for a nonlinear singular semipositone system [J]. Appl Math Comput, 2007, 192: 223- 252.
  • 10Zhang G W, Sun J X. A generalization of the cone expansion and compression fixed point theorem and appli-cations [ J]. Nonlinear Anal, 2007,67: 579-586.

同被引文献17

  • 1Wong F H. Existence of positive solutions of singular boundary value problems [J ]. Nonlinear Anal, 1993, 21: 397-406.
  • 2K S Ha, Y.H. Lee. Existence of multiple positive solutions of singular boundary value problems [J]. Nonlinear Anal, 1998, 28 37 -44.
  • 3Agarwal R P, O' Regan D. A note on existence of nonnegative solutions to singular semipositone problems [J ]. Nonlinear Anal, 1999, 36(5) : 615-622.
  • 4Ma R Y.. Positive solutions of nonlinear three-point boundary value problem [ J ]. Electron. J. Differential Equations, 1999, 34: 1-8.
  • 5D. O'Regan. Semipositone higher-order differential equations [J ]. Appl. Math. Lett, 2004, 17:201-207.
  • 6Zhang X G, Liu L S. Positive solutions of superlinear semipositone singular Dirichlet boundary value problems [J]. JMath Anal Appl, 2006, 316(2): 525-537.
  • 7Agarwal R P, O'Regan D. A coupled system of boundary value problems[J]. ApplAnal, 1998, 69: 381-385.
  • 8Xu X. Positive solutions for singular semipositone three-point systems [J]. Nonlinear Anal, 2007, 66: 791-805.
  • 9Liu L S, Zhang X G, Wu Y H. On existence of positive solution of a two point boundary problem for a nonlinear singular semi- positone system [ J ]. Appl Math Compnt, 2007, 192 : 223-232.
  • 10Guo D J, Lakshmikantham V. Nonlinear problems in abstract cones [ M ]. San Diego: Academic Press, 1998.24-56.

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淮阴师范学院学报（自然科学版）
2009年 第2期

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