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On complex Schrödinger type equations with solutions in a given domain. (English) Zbl 1486.30088

J. Contemp. Math. Anal., Armen. Acad. Sci. 56, No. 6, 368-374 (2021) and Izv. Nats. Akad. Nauk Armen., Mat. 56, No. 6, 3-11 (2021).
Summary: Value distribution, particularly the numbers of \(a\)-points, weren’t studied for meromorphic functions in a given domain which are solutions of some complex differential equations. In fact we have here a “virgin land.” A new program of investigations of similar solutions in a given domain was initiated quite recently. In this program some geometric methods were offered to study some standard problems as well as some new type problems related to Gamma-lines and Blaschke characteristic for \(a\)-points of the solutions of different equations. In this paper we apply these methods to get bounds for length of Gamma-lines and Blaschke characteristic for \(a\)-points for solutions of equations \(w^{\prime\prime}=gw^{\mu}\) considered in a given domain.

MSC:

30D30 Meromorphic functions of one complex variable (general theory)
34M04 Nonlinear ordinary differential equations and systems in the complex domain
34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
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