Convergence of formal power series solutions for some regular Gevrey-type differential equations

In this article we focus on the formal solutions for some regular Gevrey-type differential equation, with convergence of such solutions being the main point of interest. The attained results are a generalization of the classical result on the convergence of formal solutions to differential equations. The technique applied rests upon a classical argument based on a precise writing of the formal solution and a dilatation, in which several technical results on general properties of Gevrey-type sequences and Gevrey-type differential operators are applied. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/36/abstr.html