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Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations

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We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H2 spaces. It is shown that, under reasonable technical conditions, the convergence in L1 of the integral kernels implies the existence and convergence in H2 of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.

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Authors and Affiliations

  1. University of Toronto, 27 King’s College Circle, Toronto, Ontario, M5S 1A1, Canada

    V. Vougalter

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

    V. Volpert

Authors
  1. V. Vougalter
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  2. V. Volpert
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Correspondence to V. Vougalter.

Additional information

Translated from Problemy Matematicheskogo Analiza 90, January 2018, pp. 3-28.

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Vougalter, V., Volpert, V. Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations. J Math Sci 228, 601–632 (2018). https://doi.org/10.1007/s10958-017-3650-7

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  • DOI: https://doi.org/10.1007/s10958-017-3650-7

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