Existence and uniqueness of convex monotone positive solutions for boundary value problems of an elastic beam equation with a parameter - Chengbo Zhai; Chunrong Jiang (Electronic Journal of Qualitative Theory of Differential Equations, 2015)
The purpose of this paper is to investigate the existence and uniqueness of convex monotone positive solutions for a boundary value problem of an elastic beam equation with a parameter. The proofs of the main results rely on a fixed point theorem and some properties of eigenvalue problems for a class of general mixed monotone operators. The results can guarantee the existence of a unique convex monotone positive solution and can be applied to construct two iterative sequences for approximating it. Moreover, we present some pleasant properties of convex monotone positive solutions for the boundary value problem dependent on the parameter. Finally, an example is given to illustrate the main results.