Related papers: Periodic solutions of a semilinear Euler-Bernoulli…
The Lugiato-Lefever equation is a cubic nonlinear Schr\"odinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a…
The nonlinear pseudo-oscillator recently tackled by Gadella and Lara is mapped to an Emden-Fowler (EF) equation that is written as an autonomous two-dimensional ODE system for which we provide the phase-space analysis and the parametric…
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
In the dynamics of linear structures, the impulse response function is of fundamental interest. In some cases one examines the short term response wherein the disturbance is still local and the boundaries have not yet come into play, and…
In this paper, we use the variational approach to investigate recurrent properties of solutions for stochastic partial differential equations, which is in contrast to the previous semigroup framework. Consider stochastic differential…
We study a nonlinear wave equation appearing as a model for a membrane (without viscous effects) under the presence of an electrostatic potential with strength $\lambda$. The membrane has a unique stable branch of steady states…
We consider an inhomogeneous Euler-Bernoulli (EB) beam of length $L$ clamped at both ends and subject to : an external frictional damping and a thermal effect (Fourier law). We prove the well-posedness of the model and analyze the behavior…
We study the stability properties of periodic solutions to the Nonlinear Schr\"odinger (NLS) equation with a periodic potential. We exploit the symmetries of the problem, in particular the Hamiltonian structure and the $\U(1)$ symmetry. We…
The homogenization of elliptic divergence-type fourth-order operators with periodic coefficients is studied in a (periodic) domain. The aim is to find an operator with constant coefficients and represent the equation through a perturbation…
In this work, we analytically study the existence of periodic vortex cap solutions for the homogeneous and incompressible Euler equations on the rotating unit 2-sphere, which was numerically conjectured by Dritschel-Polvani and…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
We introduce the periodic Airy-Schr\"odinger operator and we study its band spectrum. This is an example of an explicitly solvable model with a periodic potential which is not differentiable at its minima and maxima. We define a…
Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of $T$-periodic solutions lying inside a bounded domain $\Omega\subset \R^N$ is,…
We study a class of linear ordinary differential equations (ODE)s with distributional coefficients. These equations are defined using an {\it intrinsic} multiplicative product of Schwartz distributions which is an extension of the…
This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…
In this paper, we address for the 2D Euler equations the existence of rigid time periodic solutions close to stationary radial vortices of type $f_0(|x|){\bf 1}_{\mathbb{D}}(x)$, with $\mathbb{D}$ the unit disc and $f_0$ being a strictly…
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
In this paper we give an extension of the Birkhoff--Lewis theorem to some semilinear PDEs. Accordingly we prove existence of infinitely many periodic orbits with large period accumulating at the origin. Such periodic orbits bifurcate from…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…