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Attractors for second order lattice dynamical systems. (English) Zbl 1002.37040
The second order lattice system \[ \ddot{u}_i+h(\dot u_i)-(u_{i-1}-2u_{i}+u_{i+1})+\lambda u_i+f(u_i)=g_i,\quad i\in \mathbb{Z}, \] is considered, where \(\lambda>0\), \((g_i)_i\in\ell^2\), and the nonlinearities \(f\) and \(g\) satisfy some regularity and monotonicity assumtpions. The existence of global attractor in a suitable state space (\(\ell^2\times\ell^2\)) is established and its semicontinuity properties are studied.

37L60 Lattice dynamics and infinite-dimensional dissipative dynamical systems
37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
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