English

On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity

Analysis of PDEs 2011-11-30 v2

Abstract

We study a qq-analog of a singularly perturbed Cauchy problem with irregular singularity in the complex domain which generalizes a previous result by S. Malek in \cite{malek}. First, we construct solutions defined in open qq-spirals to the origin. By means of a qq-Gevrey version of Malgrange-Sibuya theorem we show the existence of a formal power series in the perturbation parameter which turns out to be the qq-Gevrey asymptotic expansion (of certain type) of the actual solutions.

Keywords

Cite

@article{arxiv.1106.0401,
  title  = {On $q-$Gevrey asymptotics for singularly perturbed $q-$difference-differential problems with an irregular singularity},
  author = {Alberto Lastra and Stéphane Malek},
  journal= {arXiv preprint arXiv:1106.0401},
  year   = {2011}
}

Comments

30 pages

R2 v1 2026-06-21T18:16:40.262Z