期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

一类非线性p-Laplace边值问题的正解 被引量：1

POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR p-LAPLACIAN BOUNDARY VALUE PROBLEMS
原文传递
导出
摘要 应用锥理论和不动点指数方法,在与相应齐次增算子的第一特征值相关的条件下,得到了下述非线性p-Laplace边值问题{(|u″|p-1u″)"=f(t,u),t∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0的正解。 In this paper, we use the cone theory and the fixed point index to study the existence of positive solutions for the nonlinear p-Laplacian boundary value problems {（｜u″｜^p-4u″）″=f（t,u）,t∈（0,1） u（0）=u（1）=u″（0）=u″（1）=0 under some conditions related with the first eigenvalues corresponding to the relevant positively homogeneous operators. The results here essentially extend and improve the results existing.
作者 邹玉梅
机构地区 山东科技大学信息科学与工程学院
出处 《系统科学与数学》 CSCD 北大核心 2013年第7期841-847,共7页 Journal of Systems Science and Mathematical Sciences
基金 国家自然科学基金(10971179 11071141 61201431) 山东省优秀中青年科学家科研奖励基金(BS2010SF023 BS2012SF022)资助课题
关键词 p-Laplace边值问题 锥 不动点指数 p-Laplacian boundary value problems, cone, fixed point index.
分类号 O175.8 [理学—基础数学]
  • 相关文献

参考文献14

  • 1Agarwal R P, Lii H, O'Regan D. Eigenvalues and the one-dimensional p-Laplacian. J. Math. Anal. Appl., 2002, 266: 383-400.
  • 2Bai Z B, Ge W G. The iterative solutions for some fourth-order p-Laplacian equation boundary value problems. Appl. Math. Lett., 2006, 19: 8-14.
  • 3Feng M Q. Multiple positive solutions of fourth-order impulsive differential equations with inte- gral boundary conditions and one-dimensional p-Laplacian. Boundary Value Problems, vol. 2011, Article ID 654871, 26 pages.
  • 4Luo Y, Luo Z G. Symmetric positive solutions for nonlinear boundary value problems with - Laplacian operator. Appl. Math. Lett., 2010, 23: 657-664.
  • 5Xu J F, Yang Z L. Positive solutions for a fourth order p-Laplacian boundary value problem. Nonlinear Analysis, 2011, 74: 2612-2623.
  • 6Zhang X G, Liu L Sh. Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator. J. Math. Anal. Appl., 2007, 336: 1414-1423.
  • 7Zhang X G, Liu L Sh. A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p-Laplacian. Nonlinear Anal., 2008, 68: 3127-3137.
  • 8Zhang X M, Feng M Q, Ge W G. Symmetric positive solutions for p-Laplacian fourth-order differential equations with integral boundary conditions. J. Comput. Appl. Math., 2008, 222: 561-573.
  • 9马德香,葛渭高.具p-Laplacian算子的多点边值问题迭代解的存在性[J].系统科学与数学,2007,27(5):730-742. 被引量：5
  • 10Li Y X. Positive solutions of fourth-order boundary value problems with two parameters. J. Math. Anal. Appl., 2003, 281: 477-484.

二级参考文献10

  • 1Wang J. The existence of positive solutions for the one-dimensional p-Laplacian boundary value problem. Proc. Amer. Math. Soc., 1997, 125: 2275-2283.
  • 2He X and Ge W, Peng M. Multiple positive solutions for one-dimensional p-Laplacian boundary value problem. Applied Mathematics Letters , 2002, 15: 937-943.
  • 3Bai C and Fang J. Existence of multiple positive solutions for nonlinear m-point boundary value problem. Applied Mathematics and Computation, 2003, 140: 297-305.
  • 4Ge W and Ren J. An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacain. Nonlinear Analysis, 1998, 58(3-4): 631-644.
  • 5Mawhin J. Some boundary value problem for Hartman-type perturbations of the ordinary vector p-Laplacian. Nonlinear Analysis, 2000, 40: 497-503.
  • 6Manasevich R and Mawhin J. Periodic solutions for nonlinear systems with p-Laplacian like operator. J. Diff. Eqns., 1998, 145: 367-393.
  • 7Gaines R and Mawhin J. Coincide Degree and Nonlinear Differential Equation. Springer-Verlag: Berlin, 1977.
  • 8Guo D and Lakshmikantham V. Multiple solution of two-point boundary value problem of ordinary differential equations in Banach space. J. Math. Anal., 1998, 129: 211-222.
  • 9Ma R. Existence theorem for a second order m-point boundary value problems. Applied Mathematics Letters, 2001, 14: 1-5.
  • 10Gupta C P. A second order M-point boundary value problem at resonance. Nonlinear Analysis, 1995, 24: 1483-1489.

共引文献9

同被引文献8

引证文献1

系统科学与数学
2013年 第7期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部