Existence of resurgent solutions for equations with higher-order degeneration (Q641985)

This paper is concerned with degenerate differential equations in the form \(H(\frac{1}{k}r^{k+1}\frac{d}{dr},r)=f\) where \(k\geq 1\) and \(H(\cdot,\cdot)\) is an operator-valued symbol between two Banach spaces that is polynomial in the first argument and analytic in the second. The number \(k+1\) is called the order of degeneration. The focus of the author is on the existence of the so-called \(k\)-resurgent solutions, that is, solutions whose Borel-Laplace \(k\)-transform is endlessly continuable. The techniques employed by the author rely on the Borel-Laplace transform and its properties in the class of hyperfunctions of exponential growth.