Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 34, 2009, 145-156

GROWTH ESTIMATES FOR SOLUTIONS OF NONHOMOGENEOUS LINEAR COMPLEX DIFFERENTIAL EQUATIONS

Janne Heittokangas, Risto Korhonen and Jouni Rättyä

University of Joensuu, Mathematics
P.O. Box 111, 80101 Joensuu, Finland; janne.heittokangas 'at' joensuu.fi

University of Joensuu, Mathematics
P.O. Box 111, 80101 Joensuu, Finland; risto.korhonen 'at' joensuu.fi

University of Joensuu, Mathematics
P.O. Box 111, 80101 Joensuu, Finland; jouni.rattya 'at' joensuu.fi

Abstract. Two pointwise growth estimates are established for the solutions of

f^(k) + A_k-1(z)f^(k-1) + ... + A₁(z)f' + A₀(z)f = A_k(z),

where the coefficients A₀(z),...,A_k(z) are analytic in the disc {z : |z| < R}, 0 < R \le \infty. These pointwise estimates yield several growth estimates for the p-characteristic (generalized Nevanlinna proximity function) of the solutions. The sharpness of the results as well as some further consequences are discussed.

2000 Mathematics Subject Classification: Primary 34M10; Secondary 30D35.

Key words: Linear differential equation, growth estimate, Herold's comparison theorem, p-characteristic function.

Reference to this article: J. Heittokangas, R. Korhonen and J. Rättyä: Growth estimates for solutions of nonhomogeneous linear complex differential equations. Ann. Acad. Sci. Fenn. Math. 34 (2009), 145-156.

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