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).
Publisher
Universitat Politecnica de Valencia
Reference13 articles.
1. S. Benslimane, S. G. Georgiev and K. Mebarki, Expansion-compression fixed point theorem of Leggett-Williams type for the sum of two operators and application in three-point BVPs, Studia UBB Math, to appear.
2. G. Cain and M. Nashed, Fixed points and stability for a sum of two operators in locally convex spaces, Pacific J. Math. 39 (1971), 581-592. https://doi.org/10.2140/pjm.1971.39.581
3. S. Djebali and K. Mebarki, Fixed point index theory for perturbation of expansive mappings by k-set contraction, Topol. Meth. in Nonlinear Anal. 54, no. 2 (2019), 613-640. https://doi.org/10.12775/TMNA.2019.055
4. S. Djebali and K. Mebarki, Fixed point index on translates of cones and applications, Nonlinear Studies 21, no. 4 (2014), 579-589.
5. D. Edmunds, Remarks on nonlinear functional equations, Math. Ann. 174 (1967), 233-239. https://doi.org/10.1007/BF01360721
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献