A fixed point index theory for nowhere normal-outward compact maps and applications |
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Authors: | Guangchong Yang and Kunquan Lan |
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Institution: | College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, P. R. China and College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610225, P. R. China |
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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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Keywords: | Fixed point index fixed point theorem nowhere normal-outward map boundary value problem positive solution |
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