Related papers: Le th\'eor\`eme d'Andr\'e-Chudnovsky-Katz

We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane ({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced from no-photon QED. The associated functional is bounded from below. In the presence of…

We propose a general condition, to ensure essential self-adjointness for the Gau{\ss}-Bonnet operator, based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions or…

Using the inverse scattering method, we construct global solutions to the Novikov-Veselov equation for real-valued decaying initial data q with the property that the associated Schrodinger operator with potential q is nonnegative. Such…

We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton method…

We generalized the Korkin-Zolotarev theorem to the case of entire functions having the smallest $L^1$ norm on a system of intervals $E$. If $\bbC\setminus E$ is a domain of Widom type with the Direct Cauchy Theorem we give an explicit…

We first establish the existence of an unbounded solution to a backward stochastic differential equation (BSDE) with generator $g$ allowing a general growth in the state variable $y$ and a sub-quadratic growth in the state variable $z$,…

We study the problem of subharmonic bifurcations for analytic systems in the plane with perturbations depending periodically on time, in the case in which we only assume that the subharmonic Melnikov function has at least one zero. If the…

The Yakubovich Frequency Theorem, in its periodic version and in its general nonautonomous extension, establishes conditions which are equivalent to the global solvability of a minimization problem of infinite horizon type, given by the…

This expository paper contains a concise introduction to some significant works concerning the Karush-Kuhn-Tucker condition, a necessary condition for a solution in local optimality in problems with equality and inequality constraints. The…

We give a constructive proof of the classical Cauchy-Kovalevskaya theorem in the ODE setting which provides a sufficient condition for an initial value problem to have a unique analytic solution. Our proof is inspired by a modern functional…

The Glazman-Povzner-Wienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schr\"odinger operator $-\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its essential…

Let $G$ be a finite solvable group. We prove that if $\chi\in{\rm Irr}(G)$ has odd degree and $\chi(1)$ is the minimal degree of the non-linear irreducible characters of $G$, then $G/{\rm Ker} \chi$ is nilpotent-by-abelian.

INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…

We establish a strong unique continuation property for the subelliptic Baouendi operator under the presence of zero-order perturbations satisfying an almost Hardy-type growth condition. In particular, the admissible class includes both…

It is known that for a possibly degenerate hypoelliptic Ornstein-Uhlenbeck operator $$ L= \frac{1}{2}\text{ tr} (QD^2 ) + \langle Ax, D \rangle = \frac{1}{2}\text{ div} (Q D ) + \langle Ax, D \rangle,\;\; x \in R^N, $$ all (globally)…

We prove that near-threshold negative energy solutions to the 2D cubic ($L^2$-critical) focusing Zakharov-Kuznetsov (ZK) equation blow-up in finite or infinite time. The proof consists of several steps. First, we show that if the blow-up…

We consider the $s$-fractional Klein-Gordon equation with space-dependent damping on $\mathbb{R}^d$. Recent studies reveal that the so-called geometric control conditions (GCC) are closely related to semigroup estimates of the equation.…

We consider the defocusing fourth-order nonlinear Schr\"{o}dinger equation with potential \[ i\partial_t u + \Delta^2 u + Vu + \lambda |u|^{p-1}u = 0 \qquad (x \in \mathbb{R}^n,\ t \in \mathbb{R}), \] in dimensions $n \ge 5$. In the…

In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schr\"odinger operators $L_K+V$ with nonnegative potentials $V\in L^q_{\loc}(\BR^n)$ for $q>\f{n}{2s}$ with $0<s<1$ and $n\ge 2$; that is to say, we obtain the existence…

For smooth bounded pseudoconvex domains in $mathbb{C}^{2}$, we provide geometric conditions on (the points of infinite type in) the boundary which imply compactness of the $\bar{\partial}$-Neumann operator. It is noteworthy that the proof…