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非线性混合阶微分方程组的正解 被引量：2

Positive solutions for systems of nonlinear mixed order differential equations
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摘要 主要研究了由不同阶微分方程构成的非线性微分方程组的正解的存在性问题,通过对非线性项进行限制,运用锥理论中的不动点定理,得到了方程组正解存在性的多个结果. In this paper, the existence of positive solutions for systems of nonlinear differential equations are studied. The systems are composed of two differential equations with different order. By using fixed-point theorem of cone, various results on the existence of solutions for systems of nonlinear differential equations differential equations are established.
作者 张丽 张克梅 孙育红
机构地区 曲阜师范大学数学科学学院 德州职业技术学院计算机系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2010年第2期141-148,共8页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 山东省自然科学基金(ZR2009AL014) 国家自然科学基金(10871167)
关键词 混合边值问题 GREEN函数 不动点定理 正解 mixed boundary value problem Green＇s function fixed-point theorem positive solutions
分类号 O175.8 [理学—基础数学]
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参考文献7

  • 1Hu Ling,Wang Lianglong.Muliple positive solutions of boundary value problem for systems nonlinear second-order differential equations[J].J Math Anal Appl,2007,335:1052-1060.
  • 2Joao Mareos do O,Sebastian Lorca,Pedro Ubilla.Multiplicity of non-homogeneous fourthorder boundary value problems[J].Appl Math Lett,2008,21:279-286.
  • 3Kang Ping,Wei Zhongli.Three positive solutions of singular nonlocal boundary value problems for systems of nonlinear second-order ordinary differential equations[J].Nonlinear Anal,2009.70:444-451.
  • 4Zhou Youming,Xu Yan.Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations[J].J Math Anal Appl,2006,320:578-590.
  • 5Sun Yan.Necessary and sufficient condition for the existence of positive solutions of coupled system for elastic beams[J].J Math Anal Appl,2009,357:77-88.
  • 6Abdelkader Boucherif.Second-order boundary problems with integral boundary conditions[J].Nonlinear Anal,2009,70:364-371.
  • 7Feng Meiqiang,Ji Dehong,Ge Weigao.Positive solutions for a class of boundary value problem with intigeral boundary conditions in Banach spaces[J].Comput Appl Math,2008,222:351-363.

同被引文献13

  • 1CHENG Xiyou, ZHONG Chengkui. Existence of positive solutions for a second order ordinary differential systems[J].J Math Anal Appl, 2005, 312( 1 ) :14-23.
  • 2HU Ling, WANG Lianglong. Multiple positive solutions of for boundary value problems for systems of nonlinear second order ordinary differential [J]. J Math Anal Appl, 2007, 335 (2) :1052-1060.
  • 3HENDERSON J, NTOUYAS S K. Positive solutions for systems of nth order three point nonlocal boundary value problems[J]. Electronic Journal of Qualitative Differential Equations, 2007, 18 (1) -1-12.
  • 4LIU Yansheng, YAN Baoqiang. Multiple solutions of singular boundary value problems for differential systems[J]. J Math A- nal Appl, 2003, 287(2) :540-556.
  • 5WEI Zhongli. Positive solutions of singular Dirichlet boundary value problems for second order differential systems[J].J Math Anal Appl, 2007, 328(2):1255-1267.
  • 6YANG Zhilin. Positive solutions to a system of second order nonlocal boundary value problems[J].Nonlinear Anal, 2005, 62 ( 1 ) : 1251-1265.
  • 7ELOE P W, AHAMD B. Positive solutions of a nonlinear nth order boundary value problems with nonlocal conditions [ J ]. Applied Math Letters, 2005, 18(5) :521-527.
  • 8HAO Xin' an, LIU Lishan, WU Yonghong. Positive solutions for nonlinear nth order singular nonlocal boundary value prob- lems [ J ]. Boundary Value Problems. DOI : 10.1155/2007/74517.
  • 9CHENG Xiyou,ZHONG Chengkui.Existence of positive solutions for a second order ordinary differential systems[].JM ath Anal Appl.2005
  • 10Zhilin Yang.Positive solutions to a system of second-order nonlocal boundary value problems[].Nonlinear Analysis.2005

引证文献2

高校应用数学学报（A辑）
2010年 第2期

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