相关论文: Cantor families of periodic solutions for complete…

We prove existence of small amplitude, 2 pi/omega -periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency omega belonging to a Cantor-like set of positive measure and…

We prove existence and multiplicity of Cantor families of small amplitude analytic in time periodic solutions of the completely resonant cubic nonlinear Klein-Gordon equation on $\mathbb{S}^3$ for an asymptotically full measure set of…

We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The…

We consider the nonlinear string equation with Dirichlet boundary conditions $u_{xx}-u_{tt}=\phi(u)$, with $\phi(u)=\Phi u^{3} + O(u^{5})$ odd and analytic, $\Phi\neq0$, and we construct small amplitude periodic solutions with frequency…

Bending vibrations of thin beams and plates may be described by nonlinear Euler-Bernoulli beam equations with $x$-dependent coefficients. In this paper we investigate existence of families of time-periodic solutions to such a model using…

We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove…

We prove the existence of small amplitude periodic solutions, with strongly irrational frequency $ \om $ close to one, for completely resonant nonlinear wave equations. We provide multiplicity results for both monotone and nonmonotone…

We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…

We consider a model of nonlinear wave equations with periodically varying wave speed and periodic external forcing. By imposing non-resonance conditions on the frequency, we establish the existence of the response solutions (i.e., periodic…

In this note we present a new KAM result which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is…

We prove existence and multiplicity of small amplitude periodic solutions of the completely resonant wave equation u_tt - u_xx + f(x,u)=0 with Dirichlet boundary conditions where f(x,u)=a_2 u^2 + a_3(x) u^3 + O(u^4) or f(x,u)= a_4 u^4 +…

We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a…

In this paper we prove the existence and the stability of small-amplitude quasi-periodic solutions with Sobolev regularity, for the 1-dimensional forced Kirchoff equation with periodic boundary conditions. This is the first KAM result for a…

We prove the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is reducible to constant coefficients. This result is…

We prove an abstract Implicit Function Theorem with parameters for smooth operators defined on sequence scales, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at…

We prove existence and multiplicity of Cantor families of small amplitude time periodic solutions of completely resonant Klein-Gordon equations on the sphere $\mathbb{S}^3$ with quadratic, cubic and quintic nonlinearity, regarded as toy…

We prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T^d, d \geq 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length…

We consider a class of fully nonlinear Schr\"odinger equations and we prove the existence and the stability of Cantor families of quasi-periodic, small amplitude solutions. We deal with reversible autonomous nonlinearities and we look for…

We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under…

We study time-periodic solutions for the cubic wave equation on an interval with Dirichlet boundary conditions. We begin by following the perturbative construction of Vernov and Khrustalev and provide a rigorous derivation of the…