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 free at the other end. Some new estimates to the positive solutions to the boundary value problem are obtained. Some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established. An example is given at the end of the paper to illustrate the main results.
Yang, B. (2005). Positive solutions for a fourth order boundary value problem. Electronic Journal of Qualitative Theory of Differential Equations, 3, 1-17.