By using variational methods, we investigate the existence of T-periodic solutions to \begin{equation*} \left\{ \begin{array}{ll} [(-\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{array} \right. \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 $p\in (1, (N+2s)/(N-2s))$.
Periodic solutions for the non-local operator (−∆ + m^2)^s − m^2s with m ≥ 0 / Ambrosio, Vincenzo. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 49:1(2017), pp. 75-103. [10.12775/TMNA.2016.063]
Periodic solutions for the non-local operator (−∆ + m^2)^s − m^2s with m ≥ 0
Ambrosio, Vincenzo
2017-01-01
Abstract
By using variational methods, we investigate the existence of T-periodic solutions to \begin{equation*} \left\{ \begin{array}{ll} [(-\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{array} \right. \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 $p\in (1, (N+2s)/(N-2s))$.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
