3 papers
math.CV2026
On the existence of meromorphic solutions of the complex Schrödinger equation with a q-shift
Risto Korhonen, Wenlong Liu
In this paper, we study the following complex Schrödinger equation with a -difference term: \begin{align}\tag{â }\label{dagger} f'(z) = a(z)f(qz) + R(z, f(z)), \quad R(z, f(z)…
math.CV2025
On the extension of analytic solutions of a class of first-order q-difference equations
Wenlong Liu
In this paper, we use the Banach fixed point theorem to examine the existence of meromorphic solutions to the following first-order -difference equation \begin{align}\tag{â }\l…
math.CV2025
Transcendental meromorphic solutions and the complex Schrödinger equation with delay
Tingbin Cao, Risto Korhonen, Wenlong Liu
In this article, we focus on studying the differential-difference equation \[ f'(z) = a(z)f(z+1) + R(z, f(z)), \quad R(z, f(z)) = \frac{P(z, f(z))}{Q(z, f(z))}, \] where the two no…