Abstract
Let E be an ordered Banach space and A a continuous operator mapping some bounded order interval [ v, w] ⊂ E into itself. This paper is concerned with the number of fixed points of A on [ v, w]. There are given conditions on A and the ordering which guarantee the existence of no fixed point, precisely one, two, and more than two, distinct fixed points. The nonexistence and uniqueness theorems are completely elementary. The multiplicity results are based on the fixed-point index for α-set contractions. All of these results have applications to nonlinear integral equations and to mildly nonlinear elliptic boundary-value problems.
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