## Fisher-Kolmogorov type perturbations of the relativistic operator: differential vs. difference

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- by Petru Jebelean and Călin Şerban PDF
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## 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.## References

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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
- 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

Dedicated: Dedicated to Jean Mawhin for his 75th anniversary