Effect of resonance on the existence of periodic solutions for strongly damped wave equation. (September 2015)

• Record Type: Journal Article
• Authors: Kokocki, Piotr
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 167
• Page End: 200
• Publication Date: 2015-09
• Subjects: 37B30 -- 47J35 -- 35B34 -- 35B10; Topological degree -- Evolution equation -- Periodic solution -- Resonance; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.012
• Languages: English
• ISSNs: 0362-546X

Abstract

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.