Fixed point theorems in the study of operator equations in ordered Banach spaces and their applications

Abstract

We use fixed point index properties and the general minorant principle (see Theorem 7.B in [12]) to prove new fixed point theorems for operators leaving invariant a cone in a Banach space. Main ideas of this work are inspired from the work in [11]. The results obtained are used to prove existence of at least one positive solution to a φ−laplacian boundary value problem.