On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs





positive solution, fixed point index, cone, sum of operators, ODEs, PDEs


The aim of this work is two fold: first  we  extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction  obtained in \cite{DjebaMeb, Svet-Meb}, to  the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction.  Secondly, as  illustration of some our theoretical results,  we study  the existence of positive solutions  for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as  a class of  partial differential equations (PDEs for short).


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Author Biographies

Svetlin Georgiev Georgiev, University of Sofia

Department of Differential Equations, Faculty of Mathematics and Informatics

Karima Mebarki, University of Bejaia

Laboratory of Applied Mathematics, Faculty of Exact Sciences.


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How to Cite

S. Georgiev Georgiev and K. Mebarki, “On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs”, Appl. Gen. Topol., vol. 22, no. 2, pp. 259–294, Oct. 2021.