The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables, as introduced in [3, 15]. In particular, we characterize these expansions in terms of bounded derivatives and we develop Tauberian theorems for the summability processes involved. Furthermore, we develop and apply the Borel-Laplace analysis in this framework to prove the monomial summability of solutions of a specific class of singularly perturbed PDEs.
Supported by the Austrian FWF-Project P 26735-N25 under P. I. Armin Rainer. Partially supported by the Ministerio de Economía y Competitividad from Spain, under the Project “Ágebra y geometría en sistemas dinámicos y foliaciones singulares” (Ref.: MTM2016-77642-C2-1-P).
"Summability in a monomial for some classes of singularly perturbed partial differential equations." Publ. Mat. 65 (1) 83 - 127, 2021. https://doi.org/10.5565/PUBLMAT6512103