We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established
Yang, B. (2005). Positive solutions for the beam equation under certain boundary conditions. Electronic Journal of Differential Equations, 2005, 1-8.