Global study on analytic solutions of functional equations

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1. We have studied Riceati differential equations with doubly periodic coefficients. It was shown that all the periodic solutions are doubly periodic, Also we btained their periods and expressions.2. We have studied the distribution of zero of solutions satisfying linear differential equations with simply periodic meromorphic coefficients. Using Stokes phenomena of solutions, we gave estimates for zero-frequency of solutions of a class of equations containing Hill equations and Mathev equations.3. For Painleve transcendents (I), (II), (IV), we obtained estimates for the growth. For Painleve transcendents (III), (V) on the universal covering, we obtained estimates for the growth. For (I), we obtained a lower estimate as well. We studied the value distribution of small target as well.4. For higher order Painleve equations belonging to PI-hierarchy, we obtained a lower estimate for the frequency of poles of meromorphic solutions.