| Volume 6, Number 3, 2016, Pages 665-683 DOI：10.11948/2016044 |
| A fixed point index theory for nowhere normal-outward compact maps and applications |
| Guangchong Yang,Kunquan Lan |
| Keywords:Fixed point index,fixed point theorem,nowhere normal-outward map, boundary value problem, positive solution. |
| Abstract: |
| A fixed point index theory is developed for a class of nowhere normal-outward compact maps defined on a cone which do not necessarily take values in the cone. This class depends on the retractions on the cone and contains self-maps for any retractions, and weakly inward maps and generalized inward maps when the retraction is a continuous metric projection.
The new index coincides with the previous fixed point index theories for
compact self-maps and generalized inward compact maps.
New fixed point theorems are obtained for nowhere normal-outward compact maps and applied to treat
some abstract boundary value problems and Sturm-Liouville boundary value problems with nonlinearities
changing signs. |
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