On a Rigidity Equality for Bounded Solutions: Request for Counterexamples

<jats:p>We consider a family of non-homogeneous linear complex differential equations on $[1,\infty)$ depending on a complex parameter. Under a Rotation Number Hypothesis on the non-homogeneous term, a certain rigidity equality emerges from the asymptotic analysis. We formulate a precise statement and invite the reader to exhibit a counterexample.</jats:p>