Asymptotic expansions of solutions to the Riccati equation (Q2243699)

The scalar Riccati equation \[ y^{\prime}+\sum\limits_{j=0}^2 f_j(x) y^j=0,\quad y=y(x),\quad x, y\in \mathbb{R}, \] is investigated ,where \(f_j\), \(j\in \{0, 1, 2\}\), are uniformly absolutely convergent real power series \begin{gather*} f_j(x)= \sum\limits_{k=1}^{\infty}c_{jk}x^{p_{jk}},\quad c_{jk}, p_{jk}\in \mathbb{R},\\ p_{jk+1}< p_{jk},\quad \lim_{k\to \infty} p_{jk}=-\infty, \quad j\in \{0, 1, 2\}, \end{gather*} in a neighbourhood of \(x=\infty\). The author provides conditions under which there are extendable solutions and there are no extendable solutions for the considered Riccati equation. In the paper methods of power geometry are used.