变系数四阶边值问题正解存在性

变系数四阶边值问题正解存在性

Existence of Positive Solutions for Fourth-Order Boundary

Value Problem with Variable Coefficients

摘要/Abstract

参考文献

Metrics

数学物理学报

柴国庆;黄朝炎

湖北师范学院数学系黄石 435002

收稿日期:2005-08-18 修回日期:2006-10-24 出版日期:2007-12-25 发布日期:2007-12-25
通讯作者: 柴国庆
基金资助:
湖北省教育厅重点项目(D200722002)资助

Chai Guoqing;Huang Chaoyan

Department of Mathematics, Hubei Normal University, Huangshi 435002

Received:2005-08-18 Revised:2006-10-24 Online:2007-12-25 Published:2007-12-25
Contact: Chai Guoqing

摘要： 该文结合算子谱论,应用锥不动点定理,建立了四阶边值问题

{\begin{array}{l} u^{(4)} + B (t) u^{″} - A (t) u = f (t, u), 0 < t < 1, \\ u (0) = u (1) = u^{″} (0) = u^{″} (1) = 0 \end{array}

$\left\{ {\begin{array}{l}u^{(4)} + B(t){u}'' - A(t)u = f(t,u),0 < t < 1 ,\\u(0) = u(1) = {u}''(0) = {u}''(1) = 0 \end{array}} \right.$
正解存在性定理,这里

A (t), B (t) \in C [0, 1]

$A(t),B(t) \in C[0,1]$ ,

f (t, u) : [0, 1] \times [0, \infty) \to [0, \infty)

$f(t,u):[0,1]\times [0,\infty ) \to [0,\infty )$ 连续.

关键词: 正解, 不动点定理, 算子谱

Abstract: In this paper, by use of the fixed point
theorem, combining spectral theory of operator, the authors
establish the theorem on existence of positive solutions for
fourth-order boundary value problem with variable coefficient as
follows

{\begin{array}{l} u^{(4)} + B (t) u^{″} - A (t) u = f (t, u), 0 < t < 1, \\ u (0) = u (1) = u^{″} (0) = u^{″} (1) = 0 \end{array}

$\left\{ {\begin{array}{l} u^{(4)} + B(t){u}'' - A(t)u = f(t,u),0 < t < 1 ,\\ u(0) = u(1) = {u}''(0) = {u}''(1) = 0 \end{array}} \right.$
\noindent where

A (t), B (t) \in C [0, 1]

$A(t),B(t) \in C[0,1]$ and

f (t, u) : [0, 1] \times [0, \infty) \to [0, \infty)

$f(t,u):[0,1]\times [0,\infty ) \to[0,\infty )$ is continuous.

Key words: Positive solutions, Fixed point theorem, Operator spectra

中图分类号:

34B15

柴国庆;黄朝炎. 变系数四阶边值问题正解存在性[J]. 数学物理学报, 2007, 27(6): 1065-1073.

Chai Guoqing;Huang Chaoyan.

Existence of Positive Solutions for Fourth-Order Boundary

Value Problem with Variable Coefficients

[J]. Acta mathematica scientia,Series A, 2007, 27(6): 1065-1073.

Just accepted

Online first

Just accepted

Online first

Viewed

Full text

	From	local

	Times	39
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	95

From	Others	local

Times	74	21
Rate	78%	22%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	邹霞, 吴事良. 一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解[J]. 数学物理学报, 2018, 38(3): 496-513.
[2]	张淑琴, 胡雷. 含有变量阶导数及一个参数的非线性分数阶微分方程初值问题[J]. 数学物理学报, 2018, 38(2): 291-303.
[3]	廖家锋, 李红英. 带Sobolev临界指数的超线性Kirchhoff型方程正解的存在性与多解性[J]. 数学物理学报, 2017, 37(6): 1119-1124.
[4]	郝新安, 刘立山. 含参数四阶微分方程非局部边值问题的正解[J]. 数学物理学报, 2017, 37(2): 287-298.
[5]	董晓玉, 白占兵, 孙苏菁. 具有适型分数阶导数的边值问题的正解[J]. 数学物理学报, 2017, 37(1): 82-91.
[6]	张靖. 带有Hardy和Sobolev-Hardy临界指标项的扰动椭圆方程的解[J]. 数学物理学报, 2016, 36(3): 500-506.
[7]	黄祖达. 一类具反馈控制的时滞飞蝇方程的伪概周期解[J]. 数学物理学报, 2016, 36(3): 558-568.
[8]	夏治南. Volterra-Stieltjes型泛函积分方程解的存在性及渐近行为[J]. 数学物理学报, 2016, 36(1): 130-143.
[9]	杨芬. 全空间上一类半线性双调和方程正解的衰减[J]. 数学物理学报, 2015, 35(2): 282-287.
[10]	Diem Dang Huan, 高洪俊. 分数阶脉冲中立型随机微积分方程的适定性[J]. 数学物理学报, 2015, 35(2): 405-421.
[11]	李波, 刘菡. 一类具有扩散和交错扩散的捕食模型的正解[J]. 数学物理学报, 2014, 34(6): 1578-1586.
[12]	姚宪忠, 穆春来, 张付臣. 带双参数的半线性椭圆方程正解存在与不存在性以及一个预值结论[J]. 数学物理学报, 2014, 34(5): 1144-1150.
[13]	张文丽, 钟立楠. R^N中一类(p, q)-Laplacian椭圆方程组的多重正解[J]. 数学物理学报, 2014, 34(5): 1264-1274.
[14]	谢华朝, 李素丽. 一类非齐次临界椭圆方程在R^N中的正解[J]. 数学物理学报, 2013, 33(6): 1099-1111.
[15]	彭艳芳, 汪继秀. 一类奇异椭圆型方程的多解性[J]. 数学物理学报, 2013, 33(4): 766-776.