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In this paper, we classify the functions of small growth in the unit disc to different degree, and investigate the growth of solutions for certain linear differential equations with coefficients of small growth in the unit disc.  2004 Elsevier Inc. All rights reserved.

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The Borel exceptional value and the exponents of convergence of poles, zeros and fixed points of finite order transcendental meromorphic solutions for difference Painlevé I and II equations are estimated. And the forms of rational solutions of the difference Painlevé II equation and the autonomous difference Painlevé I equation are also given. It is also proved that the non-autonomous difference Painlevé I equation has no rational solution.