The biharmonic equation
occurs in many physical situations, most important applications are in fluid dynamics and elasticity problems [St. Bergman, M. M. Schiffer, Kernel Functions and Elliptic Differential Equations, (Academic Press, New York) (1953; Zbl 0053.39003)]. A continuous complex-valued function in a domain is biharmonic if satisfies the biharmonic equation. The paper deals with univalent and starlike biharmonic functions. If is biharmonic in any simply connected domain then it holds where and are harmonic. It is proven for example that if is biharmonic in the unit disk and it holds where is harmonic, then is starlike whenever is starlike.