Positive solutions for nonlinear operator equations and several classes of applications (Q993360)

The authors study a class of nonlinear operator equations \(x = Ax + x _{0}\) on ordered Banach spaces, where \(A\) is a monotone generalized concave operator. Employing the properties of cones and monotone iterative technique, they prove existence and uniqueness of solutions for such equations without requiring existence of upper-lower solutions and compactness and continuity conditions. Applications are proposed to first-order initial value problems and two-point boundary value problems with nonlinear term which is monotone with respect to its second argument, as well as to nonlinear systems of equations and to nonlinear matrix equations.