A new fixed point theorem in cones and applications to elastic beam equations.

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t,u(t),u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]