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math.AP2021
The existence of solutions for nonlinear elliptic equations: Simple proofs and extensions of a paper by Y. Shi
Xiaodan Xu, Rafael de la Llave, Fenfen Wang
The paper [Shi19] uses the Craig-Wayne-Bourgain method to construct solutions of an elliptic problem involving parameters. The results of [Shi19] include regularity assumptions on…
math.DS2021
Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation
Rafael de la Llave, Maria Saprykina
Consider an analytic Hamiltonian system near its analytic invariant torus carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\ma…
math.DS2021
Persistence and Smooth Dependence on Parameters of Periodic Orbits in Functional Differential Equations Close to an ODE or an Evolutionary PDE
Jiaqi Yang, Joan Gimeno, Rafael de la Llave
We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or…