Open AccessOn fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs
Author(s) -
Svetlin G. Georgiev,
Karima Mebarki
Publication year - 2021
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2021.13248
Subject(s) - mathematics , invertible matrix , ode , ordinary differential equation , lipschitz continuity , fixed point , fixed point index , pure mathematics , contraction (grammar) , expansive , fixed point theorem , class (philosophy) , mathematical analysis , differential equation , discrete mathematics , boundary value problem , medicine , compressive strength , materials science , artificial intelligence , computer science , composite material
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).