López Somoza, LucíaFernández Tojo, Fernando Adrián2022-08-032022-08-032021Journal of Fixed Point Theory and Applications 23, 69 (2021). https://doi.org/10.1007/s11784-021-00905-whttp://hdl.handle.net/10347/28999In this article we combine the study of solutions of PDEs with the study of asymptotic properties of the solutions via compactification of the domain. We define new spaces of functions on which study the equations, prove a version of Ascoli–Arzelà Theorem, develop the fixed point index results necessary to prove existence and multiplicity of solutions in these spaces and also illustrate the applicability of the theory with an exampleeng© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Topological methods for PDECompactificationExistence of solutionAscoli-Arzelà Theoremjournal article10.1007/s11784-021-00905-w1661-7746open access