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

Pages : 1018-1030

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{insert ignore into journalissuearticles values(4);}insert ignore into journalissuearticles values(x);+insert ignore into journalissuearticles values(k_{1}+k_{2});y``insert ignore into journalissuearticles values(x);+k_{1}k_{2}yinsert ignore into journalissuearticles values(x);=finsert ignore into journalissuearticles values(x,yinsert ignore into journalissuearticles values(x););, \ \ x\in insert ignore into journalissuearticles values(0,1);,\\ &yinsert ignore into journalissuearticles values(0);=y`insert ignore into journalissuearticles values(1);=y``insert ignore into journalissuearticles values(0);=y```insert ignore into journalissuearticles values(1);=0,\\ \endaligned \right. $$ 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