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

  • Vitali Vougalter
  • Vitaly Volpert
Article
  • 35 Downloads

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.

Keywords

Solvability conditions non-Fredholm operators systems of integro-differential equations stationary solutions 

Mathematics Subject Classification

35R09 35A01 35J91 

Notes

Acknowledgements

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

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Institute Camille Jordan, UMR 5208 CNRS, University Lyon 1VilleurbanneFrance
  3. 3.Peoples’ Friendship University of RussiaMoscowRussia

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