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
Vanishing, Unbounded and Angular Shifts on the Quotient of the Difference and the Derivative of a Meromorphic Function
Lasse Asikainen, Yu Chen, Risto Korhonen
We show that for a vanishing period difference operator of a meromorphic function \( f \), there exist the following estimates regarding proximity functions, \[ \lim_{η\to 0} m_η…
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…