Lower and upper solutions method for a problem of an elastic beam whose one end is simply supported and the other end is sliding clamped

Authors

MAN XU
RUYUN MA
JIN WEN

DOI

10.3906/mat-1703-10

Abstract

In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{(4)}(x)+(k_{1}+k_{2})y''(x)+k_{1}k_{2}y(x)=f(x,y(x)), \ \ x\in (0,1),\\ &y(0)=y'(1)=y''(0)=y'''(1)=0,\\ \endaligned \right. $$ which models a statically elastic beam with one of its ends simply supported and the other end clamped by sliding clamps, where $k_{1}

Keywords

Elastic beam, Green's function, lower and upper solutions, Schauder fixed point theorem

First Page

1018

Last Page

1030

Recommended Citation

XU, MAN; MA, RUYUN; and WEN, JIN (2018) "Lower and upper solutions method for a problem of an elastic beam whose one end is simply supported and the other end is sliding clamped," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 23. https://doi.org/10.3906/mat-1703-10
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/23