Existence of Multiple Periodic Solutions for a Semilinear Wave Equation in an n-Dimensional Ball

Abstract

This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an n-dimensional ball. By combining the variational methods and saddle point reduction technique, we obtain the existence of at least three periodic solutions for arbitrary space dimension n. The structure of the spectrum of the linearized problem plays an essential role in the proof, and the construction of a suitable working space is devised to overcome the restriction of space dimension.

Keywords

• existence
• periodic solutions
• wave equation
• 35l71
• 35b10