Related papers: Forced vibrations of wave equations with non-monot…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response…
We prove a global continuation result for $T$-periodic solutions of a $T$-periodic parametrized second order retarded functional differential equation on a boundaryless compact manifold with nonzero Euler-Poincare' characteristic. The…
In this paper, we investigate a class of semilinear wave equations in non-cylindrical time-dependent domains, subject to exterior homogeneous Dirichlet conditions. Under mild regularity and monotonicity assumptions on the evolving spatial…
We consider the one-dimensional nonlinear Schr\"odinger equation with Dirichlet boundary conditions in the fully resonant case (absence of the zero-mass term). We investigate conservation of small amplitude periodic-solutions for a large…
Original abstract: "We construct periodic solutions of nonlinear wave equations using analytic continuation. The construction applies in particular to Einstein equations, leading to infinite-dimensional families of time-periodic solutions…
This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known…
We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…
In this paper we construct periodic capillarity-gravity water waves with an arbitrary bounded vorticity distribution. This is achieved by reexpressing, in the height function formulation of the water wave problem, the boundary condition…
We consider the gravity water waves system with a periodic one-dimensional interface in infinite depth and we establish the existence and the linear stability of small amplitude, quasi-periodic in time, traveling waves. This provides the…
This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance:…
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…
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 +…
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing…
We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…
We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…
In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…
We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…
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…