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AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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The STUDIA UNIVERSITATIS BABEล-BOLYAI issue article summary The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name. |
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STUDIA MATHEMATICA - Issue no. 2 / 2024 | |||||||
Article: |
APPLICATION OF HAYMANโS THEOREM TO DIRECTIONAL DIFFERENTIAL EQUATIONS WITH ANALYTIC SOLUTIONS IN THE UNIT BALL. Authors: ANDRIY BANDURA. |
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Abstract: DOI: 10.24193/subbmath.2024.2.06 Received 24 December 2021; Accepted 18 January 2022. pp. 335-350 VIEW PDF FULL PDF In this paper, we investigate analytic solutions of higher order linear non-homogeneous directional differential equations whose coefficients are analytic functions in the unit ball. We use methods of theory of analytic functions in the unit ball having bounded L๐ฟ-index in direction, where L:BnโR+๐ฟ:๐ต๐โ๐ + is a continuous function such that L(z)>ฮฒ|b|1โ|z|๐ฟ(๐ง)>๐ฝ|๐|1โ|๐ง| for all zโBn,๐งโ๐ต๐, bโCnโ{0}๐โ๐ถ๐โ{0} be a fixed direction, ฮฒ>1๐ฝ>1 is some constant. Our proofs are based on application of inequalities from analog of Haymanโs theorem for analytic functions in the unit ball. There are presented growth estimates of their solutions which contains parameters depending on the coefficients of the equations. Also we obtained sufficient conditions that every analytic solution of the equation has bounded L๐ฟ-index in the direction. The deduced results are also new in one-dimensional case, i.e. for functions analytic in the unit disc. Mathematics Subject Classification (2010): 32W50, 32A10, 32A17. Keywords: analytic function, analytic solution, slice function, unit ball, directional differential equation, growth estimate, bounded $L$-index in direction |
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