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Asymptotic behavior in a general diffusive three-species predator-prey model
Families of periodic orbits for some PDE’s in higher dimensions
| 1. | Dipartimento di Matematica “F. Enriques”, Universita di Milano, Via Saldini 50, 20133 Milano, Italy, Italy |
$u_{t t} +\Delta \Delta u + m u = \psi(x, u) ,$
$\psi(x, u) = \pm u^3 + O(u^5),\quad \psi(-x,-u)=-\psi(x,u), \qquad\qquad\qquad $(1)
with Navier boundary conditions in a $n$–dimensional cube, here $\psi$ is a $C^\infty$ function, and $m$ is a positive parameter. For this equation we construct some Cantor families of periodic orbits. Our proof is very simple and is based on contraction mapping principle and on a suitable correspondence between Lyapunov Schmidt decomposition and averaging theory.
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