We study the existence and nonexistence of positive solutions for the following fourth-order two-point boundary value problem subject to nonlinear boundary conditions , where are parameters, and , and are continuous. By using the fixed-point index theory, we prove that the problem has at least one positive solution for sufficiently small and has no positive solution for large enough.
"Existence of Positive Solutions for an Elastic Beam Equation with Nonlinear Boundary Conditions." J. Appl. Math. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/972135