On bounded solutions of a problem of R. Schilling - Morawiec, Janusz (Annales Mathematicae Silesianae, 1994)
It is proved that if 0 < q ≤ (1 - ∛2 + ∛4)/3, then the zero function is the only solution f: ℝ→ℝ of (1) satisfying (2) and bounded in a neighbourhood of at least one point of the set (3).