Abstract

We study the asymptotic behaviour, as t → ∞, of bounded solutions to certain integro-differential equations in finite dimensions which include differential equations of fractional order between 0 and 2. We derive appropriate Lyapunov functions for these equations and prove that any global bounded solution converges to a steady state of a related equation, if the nonlinear potential E occurring in the equation satisfies the Łojasiewicz inequality. © 2007 Springer-Verlag.