# American Institute of Mathematical Sciences

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June  2016, 36(6): 3227-3250. doi: 10.3934/dcds.2016.36.3227

## Homotopy invariants methods in the global dynamics of strongly damped wave equation

 1 Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń

Received  May 2015 Revised  October 2015 Published  December 2015

We are interested in the following differential equation $\ddot u(t) = -A u(t) - c A \dot u(t) + \lambda u(t) + F(u(t))$ where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where the equation is at resonance at infinity, which means that $\lambda$ is an eigenvalue of $A$ and $F$ is a bounded map. We provide geometrical conditions for the nonlinearity $F$ and determine the Conley index of the set $K_\infty$, that is the union of the bounded orbits of this equation.
Citation: Piotr Kokocki. Homotopy invariants methods in the global dynamics of strongly damped wave equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3227-3250. doi: 10.3934/dcds.2016.36.3227
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