Growth of solutions of complex differential equations with entire coefficients having a multiply-connected Fatou component

Naveen Mehra (), Garima Pant () and S. K. Chanyal ()
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Naveen Mehra: Kumaun University, D.S.B. Campus
Garima Pant: Kumaun University, D.S.B. Campus
S. K. Chanyal: Kumaun University, D.S.B. Campus

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 895-906

Abstract: Abstract In this study, we show that all non-trivial solutions of $$f''+A(z)f'+B(z)f=0$$ f ′ ′ + A ( z ) f ′ + B ( z ) f = 0 have infinite order, provided that the entire coefficient A(z) has certain restrictions and B(z) has multiply-connected Fatou component. We also extend these results to higher order linear differential equations.

Keywords: Entire function; Order of growth; Multiply-connected Fatou component; 34M10; 30D35 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00311-z

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