2014/04/13 by Piotr Kokocki, Kokocki, Piotr · 2 citations
Mathematics · #35 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:35
paper · pdf · doi:10.48550/arxiv.1404.3429
23 pages. arXiv admin note: substantial text overlap with arXiv:1310.6794
arxiv created 2015/10/30 · arxiv updated 2015/11/02
We are interested in the following differential equation u(t) = -A u(t) - c A u(t) + λu(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 λ 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_∞, that is the union of the bounded orbits of this equation.