Small amplitude periodic solutions for Kirchhoff equations with Neumann conditions

Abstract

In this paper, we prove existence, regularity and local uniqueness of time-periodic solutions of Kirchhoff type equations with Neumann conditions by means of a Nash–Moser iteration scheme.

Keywords:

• Kirchhoff equation
• periodic solution
• small divisors
• Nash–Moser iteration

AMS Subject Classifications:

• 35B10
• 35L70
• 58C15

Notes

1 The author is supported by the Research Fund for the Doctoral Program of Higher Education of China [grant number 20110061120003].