On existence of quadratic differentials with poles of high orders

Conditions of existence of a quadratic differential which has poles of high orders at the points $c_k$, $k=1,\dots,p$, and is the limit of a sequence of quadratic differentials of a special type are established. The quadratic differential mentioned has no poles of order greater than 2 and has poles of order 2 at the points situated in a suitable uniform way on the circles $|z-c_k|=\varepsilon_k$, $\varepsilon_k\to0$, $k=1,\dots,p$. Bibliography: 9 titles.