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理论数学
Vol. 1 No. 2 (July 2011)
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一类四阶两点边界值问题的惰性解的存在性
Existence of Iterative Solutions of Fourth-Order Two Point Boundary Value Problems
DOI:
10.12677/pm.2011.12030
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被引量
作者:
郭英新
:
关键词:
四阶微分方程
;
两点边界值的问题
;
上下解
;
惰性解
Fourth-Order Differential Equation; Two-Point Boundary Value Problem; Lower and Upper Solutions; Iterative Solution
摘要:
利用上下解方法,得到了一类四阶两点边界值问题的惰性解的存在性。
Abstract:
In this paper, we study a class of forth-order two points’ boundary value problems. Without any nonnegative assumption, the existence of iterative solutions is obtained. Our approach is based on the lower and upper solution method.
文章引用:
郭英新. 一类四阶两点边界值问题的惰性解的存在性[J]. 理论数学, 2011, 1(2): 156-158.
http://dx.doi.org/10.12677/pm.2011.12030
参考文献
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1
]
Y. S. Yang. Fourth-order two-point boundary value problem. Proceeding of the American Mathematical Society, 1988, 104(1): 175-180.
[
2
]
M. A. Del Pino, R. F. Manasevich. Existence for fourth-order boundary value problem under a two-parameter nonresonance condition. Proceeding of the American Mathematical Society, 1991, 112(1): 81-86.
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R. Ma. Positive solutions of fourth-order two point boundary value problems. Annals of Differential Equations, 1999, 15(2): 225-231.
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B. Liu. Positive solutions of fourth-order two point boundary value problems. Applied Mathematics and Computation, 2004, 148(2): 407-420.
[
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X. Yang. Positive solutions for nonlinear singular boundary value problems. Applied Mathematics and Computation, 2002, 130(2-3): 225-234.
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K. Deimling. Nonlinear Functional Analysis. Berlin: Springer, 1985: 193-204.
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