# American Institute of Mathematical Sciences

April  2017, 37(4): 1867-1901. doi: 10.3934/dcds.2017079

## Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities

 School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received  October 2015 Revised  November 2016 Published  December 2016

Fund Project: Supported by NNSFC 11271076 and NNSFC 11121101.

The existence of 2-dimensional KAM tori is proved for the perturbed generalized nonlinear vibrating string equation with singularities $u_{tt}=((1-x^2)u_x)_x-mu-u^3$ subject to certain boundary conditions by means of infinite-dimensional KAM theory with the help of partial Birkhoff normal form, the characterization of the singular function space and the estimate of the integrals related to Legendre basis.

Citation: Chengming Cao, Xiaoping Yuan. Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities. Discrete & Continuous Dynamical Systems - A, 2017, 37 (4) : 1867-1901. doi: 10.3934/dcds.2017079
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