### Forced oscillations in strongly damped beam equation

#### Abstract

It is proved that the extensible beam equation in Ball's model

admits periodic solutions near equilibrium states if subject

to external periodic force of high frequency.

The approach is based on translation along trajectories, averaging method

and homotopy invariants such as topological degree and fixed point index.

admits periodic solutions near equilibrium states if subject

to external periodic force of high frequency.

The approach is based on translation along trajectories, averaging method

and homotopy invariants such as topological degree and fixed point index.

#### Keywords

Beam equation; periodic solution; averaging; topological degree; fixed point index

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