Fixed point results in ordered normed spaces with applications to abstract and differential equations (Q1191753)

The authors study fixed points of increasing and weakly order precompact operators which leave a conic interval in an ordered normed space invariant. The existence and construction theorems are then applied to derive existence, uniqueness, or extremality of solutions \(x\) of the operator equation \(\lambda x= y+Fx\), as well as their continuous dependence on \(\lambda\) and \(y\). Moreover, another application is provided by the periodic boundary value problem for the equation \(x'(t)= f(t,x(t))\), where \(f\) may be discontinuous in both arguments.