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New Proofs of Liouville’s Theorem and Little Picard’s Theorem for Harmonic Functions on \(R^{n} ,n\ge 2\)

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Abstract

There are several proofs for the Liouville theorem and the small Picard theorem for harmonic functions on \(R^{n} ,n\ge 2,\) in scientific literature. This paper provides a new simple proof of these theorems using the criteria of normality of harmonic functions and constancy of continuous functions on \(R^{n} ,n\ge 2.\)

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Funding

This paper is supported by the Science Support Program at the University of Montenegro and the Program Competitiveness of NRNU MEPhI.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Montenegro, Podgorica, Montenegro

    Žarko Pavićević

  2. National Research Nuclear University “MEPhI”, Moscow, Russian Federation

    Žarko Pavićević

  3. Faculty for Information Technology, University “Mediterranean”, Podgorica, Montenegro

    Miomir Andjić

Authors
  1. Žarko Pavićević
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  2. Miomir Andjić
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Correspondence to Žarko Pavićević.

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Communicated by H. Turgay Kaptanoglu.

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This article is part of the topical collection “Harmonic Analysis and Operator Theory” edited by H. Turgay Kaptanoglu, Aurelian Gheondea and Serap Oztop.

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Pavićević, Ž., Andjić, M. New Proofs of Liouville’s Theorem and Little Picard’s Theorem for Harmonic Functions on \(R^{n} ,n\ge 2\). Complex Anal. Oper. Theory 15, 93 (2021). https://doi.org/10.1007/s11785-021-01138-y

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  • DOI: https://doi.org/10.1007/s11785-021-01138-y

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