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Solvability in the Sense of Sequences for Some Non-Fredholm Operators in Higher Dimensions

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Nonlinear Dynamics, Chaos, and Complexity

Part of the book series: Nonlinear Physical Science ((NPS))

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Abstract

We study solvability of certain linear nonhomogeneous elliptic problems and establish that under reasonable technical assumptions the convergence in \(L^{2}({\mathbb R}^{d})\) of their right sides implies the existence and the convergence in \(H^{1}({\mathbb R}^{d})\) of the solutions. The equations involve the square roots of the sums of second order non-Fredholm differential operators and we rely on the methods of the spectral and scattering theory for Schrödinger type operators similarly to our earlier work [26].

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    Vitali Vougalter

  2. Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1, Villeurbanne, 69622, France

    Vitaly Volpert

Authors
  1. Vitali Vougalter
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  2. Vitaly Volpert
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Correspondence to Vitali Vougalter .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA

    Dimitri Volchenkov

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Vougalter, V., Volpert, V. (2021). Solvability in the Sense of Sequences for Some Non-Fredholm Operators in Higher Dimensions. In: Volchenkov, D. (eds) Nonlinear Dynamics, Chaos, and Complexity. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-15-9034-4_11

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  • DOI: https://doi.org/10.1007/978-981-15-9034-4_11

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-15-9033-7

  • Online ISBN: 978-981-15-9034-4

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