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The growth of solutions of complex differential equations with entire coefficient having finite deficient value

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The growth of solutions of second order complex differential equations $f''+A(z)f'+B(z)f=0$ with transcendental entire coefficients is considered. Assuming that $A(z)$ has a finite deficient value and that $B(z)$ has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

Abstract

The growth of solutions of second order complex differential equations $f''+A(z)f'+B(z)f=0$ with transcendental entire coefficients is considered. Assuming that $A(z)$ has a finite deficient value and that $B(z)$ has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

참고문헌 (25)

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