The authors study the existence and uniqueness of positive fixed points for mixed monotone operators with perturbation. They consider the existence and uniqueness of positive solutions for the operator equation
in ordered Banach spaces, where
is a mixed monotone operator and
is an increasing sub-homogeneous or
-concave operator. In fact, using the properties of cones and a fixed point theorem for mixed monotone operators, the authors obtain existence and uniqueness results for the above equation without assuming the operators to be continuous or compact. They also give some applications to boundary value problems for nonlinear fractional differential equations.