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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fisher-Kolmogorov type perturbations of the relativistic operator: differential vs. difference
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by Petru Jebelean and Călin Şerban PDF
Proc. Amer. Math. Soc. 146 (2018), 2005-2014 Request permission

Abstract:

We are concerned with the existence of multiple periodic solutions for differential equations involving Fisher-Kolmogorov perturbations of the relativistic operator of the form \begin{equation*} -\left [\phi (u’)\right ]’=\lambda u(1-|u|^q), \end{equation*} as well as for difference equations, of type \begin{equation*} -\Delta \left [\phi (\Delta u(n-1))\right ]=\lambda u(n)(1-|u(n)|^q); \end{equation*} here $q>0$ is fixed, $\Delta$ is the forward difference operator, $\lambda >0$ is a real parameter and \begin{equation*} \displaystyle \phi (y)=\frac {y}{\sqrt {1- y^2}}\quad (y\in (-1,1)). \end{equation*} The approach is variational and relies on critical point theory for convex, lower semicontinuous perturbations of $C^1$-functionals.
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Additional Information
  • Petru Jebelean
  • Affiliation: Department of Mathematics, West University of Timişoara, 4, Boulevard, V. Pârvan 300223 - Timişoara, Romania
  • MR Author ID: 217909
  • Email: petru.jebelean@e-uvt.ro
  • Călin Şerban
  • Affiliation: Department of Mathematics, West University of Timişoara, 4, Boulevard, V. Pârvan 300223 - Timişoara, Romania
  • Email: cserban2005@yahoo.com
  • Received by editor(s): June 24, 2017
  • Published electronically: January 26, 2018

  • Dedicated: Dedicated to Jean Mawhin for his 75th anniversary
  • Communicated by: Joachim Krieger
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2005-2014
  • MSC (2010): Primary 34B15, 34C25, 39A10, 39A23
  • DOI: https://doi.org/10.1090/proc/13978
  • MathSciNet review: 3767352