The Existence of Periodic Solutions for Nonlinear Beam Equations on ${\mathbb{T}}^d$ by a Para-differential Method

Abstract

This paper focuses on the construction of periodic solutions of nonlinear beam equations on the $d$-dimensional tori. For a large set of frequencies, we demonstrate that an equivalent form of the nonlinear equations can be obtained by a para-differential conjugation. Given the non-resonant conditions on each finite dimensional subspaces, it is shown that the periodic solutions can be constructed for the block diagonal equation by a classical iteration scheme.

References in corpus (3)

• KAM for reversible derivative wave equations
• Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type
• Quasi-periodic solutions to nonlinear beam equation on Compact Lie Groups with a multiplicative potential

Cited by in corpus (1)

• Periodic solutions of a semilinear Euler-Bernoulli beam equation with variable coefficients