Note on essential fixed points of approximable multivalued mappings

Fixexd point theory and applications

Lech Gó¹  Jan Andres²  rniewicz³ 

[1] University, Olomouc, Czech Republic;Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, PalackýInstitute of Mathematics, University of Kazimierz Wielki, Bydgoszcz, Poland

关键词: essential fixed points;    fixed point index;    Lefschetz number;    absolute neighborhood retracts;    approximable multivalued mappings;    J-maps;    Poincaré translation operators;    dissipative differential inclusions;    discretely essential periodic solutions;    55M20;    54C60;    55M15;    54H25;    47H04;    47H10;    34A60;    34C25;   

DOI  :  10.1186/s13663-016-0568-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A new definition of essential fixed points is introduced for a large class of multivalued maps. Two abstract existence theorems are presented for approximable maps on compact ANR-spaces in terms of a nontrivial fixed point index, or a nontrivial Lefschetz number and a zero topological dimension of the fixed point set. The second one is applied to the periodic dissipative Marchaud differential inclusions for obtaining the existence of a discretely essential subharmonic solution. Three simple illustrative examples are supplied.

【 授权许可】

CC BY