Abstract
We consider an autonomous dynamical system coming from a coupled system in cascade where the uncoupled part of the system satisfies that the solution comes from $-\infty $ and goes to $\infty $ to equilibrium points, and where the coupled part generates asymptotically a gradient-like nonlinear semigroup. Then, the complete model is proved to be also gradient-like. The interest of this extension comes, for instance, in models where a continuum of equilibrium points holds, and for example a Łojasiewicz-Simon condition is satisfied. Indeed, we illustrate the usefulness of the theory with several examples.
Citation
Eder R. Aragao-Costa. Alexandre N. Carvalho. Pedro Marín-Rubio. Gabriela Planas. "Gradient-like nonlinear semigroups with infinitely many equilibria and applications to cascade systems." Topol. Methods Nonlinear Anal. 42 (2) 345 - 376, 2013.
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