Effect of resonance on the existence of periodic solutions for strongly damped wave equation. (September 2015) - Kokocki, Piotr
Abstract: We are interested in the differential equation u ̈ ( t ) = − A u ( t ) − c A u ̇ ( t ) + λ u ( t ) + F ( t, 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 introduce new geometrical conditions for the nonlinearity F and use topological degree methods to find T -periodic solutions for this equation as fixed points of Poincaré operator.