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 : 9999-12-31

Article Type : Makaleler

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