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

Svetlin Georgiev Georgiev; Karima Mebarki

doi:10.4995/agt.2021.13248

Authors

Svetlin Georgiev Georgiev University of Sofia
Karima Mebarki University of Bejaia https://orcid.org/0000-0002-6679-5059

DOI:

https://doi.org/10.4995/agt.2021.13248

Keywords:

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

Abstract

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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