A FIXED POINT INDEX THEORY FOR NOWHERE NORMAL-OUTWARD COMPACT MAPS AND APPLICATIONS

Guangchong Yang; Kunquan Lan

doi:10.11948/2016044

2016 Volume 6 Issue 3

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Guangchong Yang, Kunquan Lan. A FIXED POINT INDEX THEORY FOR NOWHERE NORMAL-OUTWARD COMPACT MAPS AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 665-683. doi: 10.11948/2016044

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Guangchong Yang, Kunquan Lan. A FIXED POINT INDEX THEORY FOR NOWHERE NORMAL-OUTWARD COMPACT MAPS AND APPLICATIONS[J]. Journal of Applied Analysis & Computation, 2016, 6(3): 665-683. doi: 10.11948/2016044

A FIXED POINT INDEX THEORY FOR NOWHERE NORMAL-OUTWARD COMPACT MAPS AND APPLICATIONS

College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, P. R. China;Department of Mathematics, Ryerson University, Toronto, Ontario, Canada M5B 2K3

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Abstract

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.
- Fixed point index /
- fixed point theorem /
- nowhere normal-outward map /
- boundary value problem /
- positive solution
MSC: 47H11;34B18;47H10;47H30

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