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算子方程Lx=Nx的正解 被引量：7

Positive Solutions of a Class of Operator Equations Lx=Nx
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摘要 该文把迭合度的概念推广到算子L-N在锥上的零点指数.利用锥理论给出了零点指数的一些计算方法和算子方程解的存在性定理,并应用到m点边值非局部共振问题非负解的存在性. In this paper, the concept about coincidence degree is generalized to the zero point index of L - N operators in cones. Some methods of computation of the zero point index and the existence theorems of operator equations are given by making use of the theory of cones and applied to investigate the existence of nonnegative solutions for the second order ordinary differential equation of m-point nonlocal boundary value problems at resonance.
作者 王峰 孙经先 崔玉军
机构地区 江苏工业学院数理学院 徐州师范大学数学科学学院 山东科技大学信息科学与工程学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2010年第1期278-288,共11页 Acta Mathematica Scientia
基金 国家自然科学基金(10971179)资助
关键词 零点指数 FREDHOLM算子 锥 边值问题 共振. Zero point index Fredholm operators Cone Boundary value problems Resonance.
分类号 O175.14 [理学—基础数学]
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参考文献10

  • 1Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations. Berlin, New York: Springer-Verlag, 1977.
  • 2Mawhin J L. Topological Degree Methods in Nonlinear Boundary Value Problems. Providence, RI: Amer Math Soc, 1979.
  • 3郭大钧,孙经先.非线性常微分方程泛函方法[M].济南:山东科学技术出版社,1994.115-119.
  • 4Cremins C T. A fixed-point index and existence theorems for semilinear equations in cones. Nonlinear Anal, 2001, 46:789-806.
  • 5郭大钧.非线性泛函分析.济南:山东科学技术出版社,2003
  • 6Feng W. On a m-point boundary value problems. Nonlinear Anal, 1997, 30:5369-5374.
  • 7Ma Ruyun. Existence theorems for a second order m-point boundary value problem. J Math Anal Appl, 1997, 211:545-555.
  • 8Ma Ruyun. Existence results of a m-point boundary value problem at resonance. J Math Anal Appl, 2004, 294:147-157.
  • 9马宇红,马如云.一类奇异非线性三点边值问题的正解[J].数学物理学报（A辑）,2003,23(5):583-588. 被引量：26
  • 10马如云.Robin型二阶m-点边值问题正解的存在性[J].数学物理学报（A辑）,2004,24(3):307-318. 被引量：3

二级参考文献11

  • 1Feng W, Webb J R L. Solvability of m-point boundary value problems with nonlinear growth. J Math Anal Appl,1997, 212:467-480
  • 2Gupta C P. Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation. J Math Anal Appl, 1992, 168:540-551
  • 3Gupta C P. A sharper condition for the solvability of a three-point second order boundary value problem. J Math Anal Appl, 1997, 205:579-586
  • 4Gupta C P, Ntouyas S K, Tsamatos P Ch. Solvability of an m-point boundary value problem for second order ordinary differential equations. J Math Anal Appl, 1995, 189: 575-584
  • 5Il'in V A, Moiseev E I. Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects. Differential Equations,1987, 23(7): 803-810
  • 6Ruyun Ma. Existence theorems for a second order m-point boundary-value problem. J Math Anal Appl, 1997,211: 545-555
  • 7Ruyun Ma. Positive solutions for second-order three-point boundary-value problems. Applied Mathematics Letters, 2001, 14:1-5
  • 8Hai D D. Positive solutions for semilinear elliptic equations in annular. Nonlinear Analysis, 1999, 37: 1051-1058
  • 9Dang H, Schmitt K. Existence of positive solutions for semilinear elliptic equations in annular domains. Differential and Integral Equations, 1994, 7(3): 747-758
  • 10Feng W, Webb J R L. Solvability of three-point boundary value problems at resonace. Nonlinear Analysis TMA,1997, 30(6): 3227-3238

共引文献30

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二级引证文献6

数学物理学报（A辑）
2010年 第1期

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