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2017 Periodic solutions for the non-local operator $(-\Delta+m^{2})^{s}-m^{2s}$ with $m\geq 0$
Vincenzo Ambrosio
Topol. Methods Nonlinear Anal. 49(1): 75-103 (2017). DOI: 10.12775/TMNA.2016.063


By using variational methods, we investigate the existence of $T$-periodic solutions to \begin{equation*} \begin{cases} [(-\Delta_{x}+m^{2})^{s}-m^{2s}]u=f(x,u) &\mbox{in } (0,T)^{N}, \\ u(x+Te_{i})=u(x) &\mbox{for all } x \in \mathbb{R}^N, \ i=1, \dots, N, \end{cases} \end{equation*} where $s\in (0,1)$, $N> 2s$, $T> 0$, $m\geq 0$ and $f$ is a continuous function, $T$-periodic in the first variable, verifying the Ambrosetti-Rabinowitz condition, with a polynomial growth at rate $p\in (1, ({N+2s})/({N-2s}))$.


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Vincenzo Ambrosio. "Periodic solutions for the non-local operator $(-\Delta+m^{2})^{s}-m^{2s}$ with $m\geq 0$." Topol. Methods Nonlinear Anal. 49 (1) 75 - 103, 2017.


Published: 2017
First available in Project Euclid: 11 April 2017

zbMATH: 06773117
MathSciNet: MR3635638
Digital Object Identifier: 10.12775/TMNA.2016.063

Rights: Copyright © 2017 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.49 • No. 1 • 2017
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