二阶半正微分方程三点边值问题的正解
Positive Solution for Second-Order Singular Semipositone Differential Equations Three-Point Boundary Value Problems
摘要:
利用锥拉伸与压缩不动点定理讨论了一类奇异半正二阶微分方程的三点边值问题,得到了正解存在的一个充分条件,并且给出了正解存在的范围。
Abstract:
Using the Krasnoselskii’s fixed point theorem on compression and expansion of cone, this paper investigates a class of second-order singular semipositone differential equations with three-point boundary value problems; a sufficient and the existent range of positive solutions are given.
参考文献
|
[1]
|
Zhao, Z. and Zhang, X. (2007) C(I)Positive Solutions of Nonlinear Singular Differential Equations for Nonmonotonic Function Terms. Nonlinear Analysis, 66, 22-37.
|
|
[2]
|
赵增勤. 一类非线性奇异微分方程正解的存在性定理[J]. 数学物理学报, 2005, 25A(3): 393-403.
|
|
[3]
|
刘衍胜. Banach空间中非线性奇异微分方程边值问题的正解[J]. 数学学报, 2004, 47(1): 131-140.
|
|
[4]
|
Xu, X. (2007) Possitive Solutions for Singular Semi-Positone Three-Point Systems. Nonlinear Analysis, 66, 791-805. [Google Scholar] [CrossRef]
|
|
[5]
|
陈祥平, 赵增勤. 一类半正奇异二阶脉冲微分方程的正解[J]. 高校应用数学学报, 2009A(3): 281-289.
|
|
[6]
|
Zhang, X.G., Liu, L.S. and Wu, Y.H. (2007) Existence of Positive Solutions for Second-Order Se-mipositone Differential Equations on the Half-Line. Applied Mathematics and Computation, 185, 628-635. [Google Scholar] [CrossRef]
|
|
[7]
|
陈祥平, 赵增勤. 一类奇异脉冲微分方程周期边值问题的多解性[J]. 应用数学, 2009(3): 559-565.
|
|
[8]
|
Guo, D. and Lakshmikantham, V. (1988) Nonlinear Problems in Abstract Cones. Academic Press, San Diego.
|