Long-time behavior of bounded global solutions to systems of nonlinear integro-differential equations

Article type: Research Article

Authors: Sánchez, Justino^; | Vergara, Vicente

Affiliations: Departamento de Matemáticas, Universidad de la Serena, La Serena, Chile. E-mail: jsanchez@userena.cl | Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile. E-mail: vvergaraa@uta.cl

Note: [] Corresponding author: Justino Sánchez, Departamento de Matemáticas, Universidad de la Serena, Avda. Cisternas 1200, La Serena, Chile. E-mail: jsanchez@userena.cl

Abstract: We study the long-time behavior of bounded solutions of certain systems of nonlinear integro-differential equations, including differential equations of fractional order between 1 and 2. We obtain appropriate Lyapunov functions for this system and prove that any bounded global solution converges to a steady state if the nonlinear potential E occurring in the system satisfies the Łojasiewicz inequality.

Keywords: integro-differential equations, fractional derivative, gradient system, Lyapunov function, convergence to steady state, Łojasiewicz inequality

DOI: 10.3233/ASY-131180

Journal: Asymptotic Analysis, vol. 85, no. 3-4, pp. 167-178, 2013