On nonnegative radial entire solutions of second order quasilinear elliptic systems.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
Oscillations of anharmonic Fourier series and the wave equation.
In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of⎧ utt + (-1)m Δmu = 0 (t,x) ∈ R x Ω⎨⎩ u|Γ = ... = Δm-1 u|Γ = 0 t ∈ R.These results rely on the study of a sign of almost periodic functions of a special form restricted to a bounded interval J.
Periodic and aqlmost-periodic solutions of semihnear equations in Banach spaces.
Quasi Periodic Solutions of Nonlinear Random Schrödinger Equations
Quasi-periodic solutions for a nonlinear wave equation.
Quasi-periodic solutions of nonlinear random Schrödinger equations
Quasi-periodic solutions of PDEs
The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in , , and the - derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.
Quasi-periodic solutions with Sobolev regularity of NLS on with a multiplicative potential
We prove the existence of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on , finitely differentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are then the solutions are . The proofs are based on an improved Nash-Moser iterative scheme, which assumes the weakest tame estimates for the inverse linearized operators...
Solutions presque périodiques des inéquations d'évolution avec des fonctionnelles non différentiables
Stability of unique pseudo almost periodic solutions with measure
By means of the fixed-point methods and the properties of the -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where is a positive measure. A numerical example is given to illustrate our main results.
Sur la solution bornée et presque périodique des inéquations d'évolution paraboliques
Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDP
Lorsque tous les champs caractéristiques d’un système hyperbolique riche sont linéairement dégénérés, les opérateurs résolvants sont bien définis et opèrent sur l’ensemble des solutions de certains systèmes d’équations différentielles ordinaires. Celles-ci peuvent être implicites ou explicites. Dans le cas implicite, on montre que toutes les solutions sont presque-périodiques; de plus elles seront toutes périodiques pourvu que l’une d’entre elles le soit. Dans le cas explicite, on définit un opérateur...
The cubic Szegő equation
We consider the following Hamiltonian equation on the Hardy space on the circle,where is the Szegő projector. This equation can be seen as a toy model for totally non dispersive evolution equations. We display a Lax pair structure for this equation. We prove that it admits an infinite sequence of conservation laws in involution, and that it can be approximated by a sequence of finite dimensional completely integrable Hamiltonian systems. We establish several instability phenomena illustrating...
Vibrations de classe Cs 2 des tores plats de dimension s et théorie des nombres.
Критарий поточечной стабилизации для параболических уравнений второго порядка с почти-периодическими коэффициентами
О восстановлении переменных действий для уравнения КдФ в классе почти периодических функций по счетному набору полиномиальных законов сохранения
Об устранимых особенностях ограниченных решений квазилинейных эллиптических уравнений любого порядка
Ограниченные и почти периодические решения эволюционных вариационных неравенств
Ограниченные и почти-периодические по времени решения одного класса нелинейных эволюционных уравнений