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

作者：Yang, Guangchong^*; Lan, Kunquan

来源：Journal of Applied Analysis and Computation, 2016, 6(3): 665-683.

DOI：10.11948/2016044

• Fixed point index
• fixed point theorem
• nowhere normal-outward map
• boundary value problem
• positive solution

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.

• 出版日期2016-8
• 单位成都信息工程大学