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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, Man Xu, Ruyun Ma, Jin Wen
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, Man Xu, Ruyun Ma, Jin Wen
Turkish Journal of Mathematics
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}