Related papers: Decidability of the HD0L ultimate periodicity prob…

We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…

In this paper, we consider the problem of determining the \emph{exact} number of periodic orbits for polynomial planar flows. This problem is a variant of Hilbert's 16th problem. Using a natural definition of computability, we show that the…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…

For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to $-\Delta u + |Du|^\gamma = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q > d \frac{\gamma-1}\gamma$.

We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…

We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for continuously differentiable initial data. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski…

We show that any measurable solution of the cohomological equation for a H\"older linear cocycle over a hyperbolic system coincides almost everywhere with a H\"older solution. More generally, we show that every measurable invariant…

We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

This paper introduces a notion of viscosity solutions for second order elliptic Hamilton-Jacobi-Bellman (HJB) equations with infinite delay associated with infinite-horizon optimal control problems for stochastic differential equations with…

In this paper we consider the first order discrete Hamiltonian system $$\begin{cases} x_1(n+1)-x_1(n)& =- H_{x_2}(n,x(n)), x_2(n)-x_2(n-1)& =\ \ H_{x_1}(n,x(n)). \end{cases} $$ Where $n\in \mathbb{Z}$, $x(n)=$ $x_1 (n) \choose x_2 (n)$$ \in…

The square-free word problem relative to a system of two defining relations is decidable.

We present an illustrative application of the two famous mathematical theorems in differential topology in order to show the existence of periodic orbits with arbitrary given period for a class of hamiltonians .This result point out for a…

This paper investigates the scattering of biharmonic waves by a one-dimensional periodic array of cavities embedded in an infinite elastic thin plate. The transparent boundary conditions are introduced to formulate the problem from an…

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…

We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.

We provide a simple proof of the existence of dark solitons of the defocusing cubic nonlinear Schrodinger equation with periodic inhomogeneous nonlinearity. Moreover, our proof allows for a broader class of inhomogeneities and gives some…

The main goal of this paper is twofold. First, it characterizes the existence of positive periodic solutions for a general class of weighted periodic-parabolic logistic problems of degenerate type (see (1.1)). This result provides us with…

We prove that if $\pi$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $\pi$-groups. In particular, when $\pi$ is the empty set, we obtain Henckell's decidability of…