Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 22, Number 2 (2015), 177-198.
Poincaré's problem in the class of almost periodic type functions
We consider the Poincaré's classical problem of approximation for second order linear differential equations in the class of almost periodic type functions. We obtain an explicit form for solutions of these equations by studying a Riccati equation associated with the logarithmic derivative of a solution. The fixed point Banach argument allows us to find almost periodic and asymptotically almost periodic solutions of the Riccati equation. A decomposition property of the perturbations induces a decomposition on the Riccati equation and its solutions. In particular, by using this decomposition we obtain asymptotically almost periodic and also $p$-almost periodic solutions to the Riccati equation.
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 2 (2015), 177-198.
First available in Project Euclid: 28 May 2015
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Figueroa, Pablo; Pinto, Manuel. Poincaré's problem in the class of almost periodic type functions. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 177--198. doi:10.36045/bbms/1432840857. https://projecteuclid.org/euclid.bbms/1432840857