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OMEGA LIMIT SETS IN POSITIVE CONES
Published online by Cambridge University Press: 23 December 2003
Abstract
The omega limit sets of a nonlinear operator $T$ which is defined on a positive cone and satisfies certain ray-contractive type conditions are discussed. Under the assumption that the restriction of $T$ to a compact subset is surjective, the following alternatives are proved: the omega limit set of a point in the cone either consists of a fixed point or forms a 2-cycle. In addition, new proofs and extensions to relevant results are given.
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- © The London Mathematical Society 2004
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