English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We are interested in the differential equation $\ddot u(t) = -A u(t) - c A\dot u(t) + \lambda u(t) + F(t,u(t))$, where $c > 0$ is a damping factor, $A$is a sectorial operator and $F$ is a continuous map. We consider the situationwhere the equation is at resonance at infinity, which means that $\lambda$ isan eigenvalue of $A$ and $F$ is a bounded map. We introduce new geometricalconditions for the nonlinearity $F$ and use topological degree methods to find$T$-periodic solutions for this equation as fixed points of Poincar\'eoperator.

Effect of resonance on the existence of periodic solutions for strongly damped wave equation