article

Upper and lower solution method for fourth-order four-point boundary value problems

Authors:

De-xiang Ma,

Xiao-zhong YangAuthors Info & Claims

Journal of Computational and Applied Mathematics, Volume 223, Issue 2

Pages 543 - 551

https://doi.org/10.1016/j.cam.2007.10.051

Published: 20 January 2009 Publication History

Abstract

This paper is concerned with the fourth-order four-point boundary value problem {u^(^4^)(t)+f(t,u,u^'')=0,t@?[0,1]=I,u(0)=0,u(1)=au(@h),u^''(0)=0,u^''(1)=bu(@x), where @h,@x@?(0,1) and a,b>=0. The upper and lower solution method and a new maximum principle are employed to establish existence results and we release the increasing condition imposed on f(t,u,v).

References

[1]

Leea, S., Monotone method for second order periodic boundary value problem. Nonlinear Anal. v7. 349-355.

Crossref

Google Scholar

[2]

Ma, R.Y., Zhang, J.H. and Fu, S.M., The method of lower and upper solutions for fourth-order two-point boundary value problem. J. Math. Anal. Appl. v215. 415-422.

Google Scholar

[3]

Zhang, Z.X. and Wang, J., The upper and lower solution method for a class of singular nonlinear second order three-point boundary value problems. J. Comput. Appl. Math. v147. 41-52.

Digital Library

Google Scholar

[4]

Cabada, A., The method of lower and upper solutions for second, third, fourth and higher order boundary value problems. J. Math. Anal. Appl. v185. 302-320.

Crossref

Google Scholar

[5]

Zhang, Q., Chen, S. and Lü, J., Upper and lower solution method for fourth-order four-point boundary value problems. J. Comput. Appl. Math. v196. 387-393.

Digital Library

Google Scholar

Cited By

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Xu MLin YWang Y(2016)A new algorithm for nonlinear fourth order multi-point boundary value problemsApplied Mathematics and Computation10.1016/j.amc.2015.10.041274:C(163-168)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1016/j.amc.2015.10.041
Wang YWu WAgarwal R(2011)A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problemsComputers & Mathematics with Applications10.1016/j.camwa.2011.04.01661:11(3226-3245)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1016/j.camwa.2011.04.016
Wang Y(2010)On 2nth-order nonlinear multi-point boundary value problemsMathematical and Computer Modelling: An International Journal10.1016/j.mcm.2010.01.00851:9-10(1251-1259)Online publication date: 1-May-2010
https://dl.acm.org/doi/10.1016/j.mcm.2010.01.008

Index Terms

Upper and lower solution method for fourth-order four-point boundary value problems
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations
    2. Numerical analysis
      1. Numerical differentiation
2. Theory of computation
  1. Design and analysis of algorithms

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Information

Published In

cover image Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics Volume 223, Issue 2

January, 2009

542 pages

ISSN:0377-0427

Issue’s Table of Contents

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 20 January 2009

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Cited By

View all

Xu MLin YWang Y(2016)A new algorithm for nonlinear fourth order multi-point boundary value problemsApplied Mathematics and Computation10.1016/j.amc.2015.10.041274:C(163-168)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1016/j.amc.2015.10.041
Wang YWu WAgarwal R(2011)A fourth-order compact finite difference method for nonlinear higher-order multi-point boundary value problemsComputers & Mathematics with Applications10.1016/j.camwa.2011.04.01661:11(3226-3245)Online publication date: 1-Jun-2011
https://dl.acm.org/doi/10.1016/j.camwa.2011.04.016
Wang Y(2010)On 2nth-order nonlinear multi-point boundary value problemsMathematical and Computer Modelling: An International Journal10.1016/j.mcm.2010.01.00851:9-10(1251-1259)Online publication date: 1-May-2010
https://dl.acm.org/doi/10.1016/j.mcm.2010.01.008

Abstract

References

Cited By

Index Terms

Recommendations

Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem