Fixed points of increasing operators in ordered Banach spaces and applications

Abstract

In this paper, we prove some fixed point theorems of increasing operators which map an order interval into itself. Compactness conditions on the operator are removed by assuming the space to be weakly complete or assuming the operator to have some concavity or convexity properties. some results of M. A. Krasnoselskii and H. Amann are generalized. The abstract results are used to get some existence theorems for ODEs in Banach spaces.

Keywords:

• Fixed point cone
• increasing operator
• nonlinear ODES in Banach spaces

AMS (MOS)::

• 47H
• 34K30