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On the Existence in the Sense of Sequences of Stationary Solutions for Some Systems of Non-Fredholm Integro-differential Equations

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Abstract

We prove the existence in the sense of sequences of stationary solutions for some systems of reaction–diffusion type equations in the appropriate \(H^{2}\) spaces. It is established that, under reasonable technical conditions, the convergence in \(L^{1}\) of the integral kernels yields the existence and the convergence in \(H^{2}\) of the solutions. The nonlocal elliptic problems contain the second-order differential operators with and without Fredholm property.

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Acknowledgements

The work was partially supported by the RUDN University Program 5-100.

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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, 69622, Villeurbanne, France

    Vitaly Volpert

  3. Peoples’ Friendship University of Russia, Ulitsa Miklukho-Maklaya, 6, Moscow, 117198, Russia

    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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Vougalter, V., Volpert, V. On the Existence in the Sense of Sequences of Stationary Solutions for Some Systems of Non-Fredholm Integro-differential Equations. Mediterr. J. Math. 15, 205 (2018). https://doi.org/10.1007/s00009-018-1248-z

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