变系数四阶边值问题正解存在性

PDF (PC)

Existence of Positive Solutions for Fourth-Order Boundary Value Problem with Variable Coefficients

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

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

CLC Number:

34B15

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.

0
/ Save 0 / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: http://121.43.60.238/sxwlxbA/EN/

http://121.43.60.238/sxwlxbA/EN/Y2007/V27/I6/1065

Trendmd

[1]	Zou Xia, Wu Shiliang. Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence [J]. Acta mathematica scientia,Series A, 2018, 38(3): 496-513.
[2]	Liao Jiafeng, Li Hongying. Existence and Multiplicity of Positive Solutions for the Superlinear Kirchhoff-Type Equations with Critical Sobolev Exponent [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1119-1124.
[3]	Guo Tingguang, Xu Zhiting. Existence of Traveling Waves in a Spatial Infectious Disease Model with Vaccination [J]. Acta mathematica scientia,Series A, 2017, 37(6): 1129-1147.
[4]	Diem Dang Huan, Gao Hongjun. Well-Posedness for Fractional Neutral Impulsive Stochastic Integro-Differential Equations [J]. Acta mathematica scientia,Series A, 2015, 35(2): 405-421.
[5]	LI Bo, LIU Han. Positive Solutions of the Predator-Prey Model with Diffusion and Cross Diffusion [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1578-1586.
[6]	ZHANG Wen-Li, ZHONG Li-Nan. Multiplicity of Positive Solutions for a (p, q-Laplacian Elliptic Systems in R^N [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1264-1274.
[7]	Dumitru MOTREANU, Abdelkrim MOUSSAOUI. A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE [J]. Acta mathematica scientia,Series A, 2014, 34(3): 905-916.
[8]	XIE Hua-Chao, LI Su-Li. Positive Solutions for An Inhomogeneous Singular Elliptic Equation with Critical Exponent in R^N [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1099-1111.
[9]	PENG Yan-Fang, WANG Ji-Xiu. Multiplicity of Solutions for a Singular Equation [J]. Acta mathematica scientia,Series A, 2013, 33(4): 766-776.
[10]	SUN Sheng, WANG Fang-Lei, AN Yu-Kun. Strong Approximations of Linear Processes [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1050-1055.
[11]	ZHANG Xin-Guang, PAN Chuan-Zhong. Exsitence of Multiple Positive Solutions for a Semipositone Nonlinear Multi-point Boundary Value Problems [J]. Acta mathematica scientia,Series A, 2012, 32(5): 996-1010.
[12]	YAO Qiang-Liu. Positive Solutions of \|Second-Order Singular Periodic Differential Systems [J]. Acta mathematica scientia,Series A, 2012, 32(3): 576-587.
[13]	ZHANG Ruo-Jun, WANG Lin-Shan. Almost Periodic Solutions for Cellular Neural Networks with Distributed Delays [J]. Acta mathematica scientia,Series A, 2011, 31(2): 422-429.
[14]	YAN Bao-Qiang. The Nonexistence and Existence of Singular Three-point Boundary Value Problems \|with Sign-changing Nonlinearities [J]. Acta mathematica scientia,Series A, 2011, 31(1): 34-52.
[15]	ZHAO Jun-Fang, GE Wei-Gao. Triple Positive Solutions of 2m-point Boundary Value Problem of Sturm-Liouville Type with one Dimensional p-Laplacian [J]. Acta mathematica scientia,Series A, 2011, 31(1): 92-102.

Viewed

Full text

	From	local

	Times	39
	Rate	100%

Abstract

101

Just accepted	Online first	Issue

0	0	101

From	Others	local

Times	78	23
Rate	77%	23%

Cited

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


This page requires you have already subscribed to WoS.

Shared

Discussed

[1]	Chen Xuegang; Sun Liang; Xing Huaming. Paired-domination Number in Cubic Graphs[J]. Acta mathematica scientia,Series A, 2007, 27(1): 166 -170 .
[2]	Liu Jicheng. A Generalization of Strassen's Theorem for Brownian Motion [J]. Acta mathematica scientia,Series A, 2006, 26(4): 485 -492 .
[3]	Chen Zhenlong; Li Huiqiong. Holder Laws and Multiple Points for Self-intersection Local Time Increments of Generalized α-stable Process[J]. Acta mathematica scientia,Series A, 2006, 26(2): 241 -250 .
[4]	Zhao Wenhui;Gao Yan. Second-order Optimality Conditions for C^1,1 Semidefinite Programming [J]. Acta mathematica scientia,Series A, 2008, 28(1): 155 -163 .
[5]	Lin Jinguan; Wei Bocheng. Testing for Homogeneity of Between-individual Variances and Autocorrelation Coefficients in Longitudinal Nonlinear Models with Random Effects and AR(1) Errors [J]. Acta mathematica scientia,Series A, 2008, 28(2): 291 -301 .
[6]	Li Cheng;Liu Lishan. Three Nontrival Positive Solutions for Second Order Three Point Boundary Value Problems with Sign Changing Nonlinearities[J]. Acta mathematica scientia,Series A, 2008, 28(3): 515 -522 .
[7]	Peng Zhigang. The Extreme Points of a Class of Analytic Operator-valued Functions[J]. Acta mathematica scientia,Series A, 2008, 28(5): 945 -957 .
[8]	WANG Wei-Hong, WU Huo-Xiong. Weighted Weak Type Estimates for Commutators of \|Fractional Integrals on Spaces of Homogeneous Type[J]. Acta mathematica scientia,Series A, 2009, 29(3): 553 -563 .
[9]	HU Guo-En, ZHANG Qi-Hui. A Two-weight Norm Inequality for Singular Integral Operators with Non-smooth Kernel on Spaces of Homogeneous Type[J]. Acta mathematica scientia,Series A, 2009, 29(3): 764 -772 .
[10]	SUN Ming-Chao. Quantum Entropy of the Electromagnetic Field in Vaidya Bonner de Sitter Black Hole[J]. Acta mathematica scientia,Series A, 2005, 25(1): 67 -72 .

Abstract
References
Related Articles
Metrics
Comments
Recommended

TOP

Just accepted

Online first

Just accepted

Online first