相关论文: Le th\'eor\`eme d'Andr\'e-Chudnovsky-Katz

In this article we present some results on the existence of positive and ground state solutions for the nonlinear Klein-Gordon-Maxwell equations. We introduce a general nonlinearity with subcritical and supercritical growth which does not…

The Cauchy problem for the Zakharov system in the energy-critical dimension $d=4$ is considered. We prove that global well-posedness holds in the full (non-radial) energy space for any initial data with energy and wave mass below the ground…

The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…

This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…

In the context of the Kasparov product in unbounded KK-theory, a well-known theorem by Kucerovsky provides sufficient conditions for an unbounded Kasparov module to represent the (internal) Kasparov product of two other unbounded Kasparov…

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the…

In this paper, let $G$ be a Cayley graph of a discrete group of polynomial growth with homogeneous dimension $N\geq3$. We study the Choquard type equation on $G$: \begin{equation} \Delta u+(R_{\alpha}\ast\mid u\mid^{p})\mid u\mid^{p-2}u=0,…

The Cauchy-Davenport theorem states that for any two nonempty subsets A and B of Z/pZ we have |A+B| >= min{p,|A|+|B|-1}, where A+B:={a+b (mod p) | a in A, b in B}. We generalize this result from Z/pZ to arbitrary finite (including…

Consider in a real Hilbert space $H$ the differential equation (inclusion) $(E)$: $p(t)u^{\prime \prime}(t)+q(t)u^{\prime}(t)\in Au(t)+f(t)$ for a.a. $t>0$, with the condition $(B)$: $u(0)=x \in \overline{D(A)}$, where $A\colon D(A)\subset…

We investigate existence and asymptotic completeness of the wave operators for nonlinear Klein-Gordon and Schr\"odinger equations with a defocusing exponential nonlinearity in two space dimensions. A certain threshold is defined based on…

The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated. When the initial data is a small perturbation of an equilibrium state, global existence and optimal temporal decay estimates…

Boshernitzan found a decay condition on the measure of cylinder sets that implies unique ergodicity for minimal subshifts. Interest in the properties of subshifts satisfying this condition has grown recently, due to a connection with the…

A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be…

We establish the uniqueness of large solutions to the non-cutoff Boltzmann equation with moderate soft potentials. Specifically, the weak solution $F=\mu+\mu^{\frac{1}{2}}f$ is unique as long as it has finite energy, in the sense that the…

The discrete Schr\"odinger operator with the Dirichlet boundary condition is considered on the half-line lattice $n\in \{1,2,3,\dots\}.$ It is assumed that the potential belongs to class $\mathcal A_b,$ i.e. it is real valued, vanishes when…

We study neutral functional differential equations with stable linear non-autonomous $D$-operator. The operator of convolution $\hat{D}$ transforms $BU$ into $BU$. We show that, if $D$ is stable, then $\hat{D}$ is invertible and, besides,…

We consider the $\dbar-$ equation in $\C^1$ in classes of functions with Gaussian decay at infinity. We prove that if the right-hand side of the equation is majorated by $\exp(-q|z|^2)$, with some positive $q$, together with derivatives up…

We consider a quasinilpotent operator whose resolvent is entire operator function of exponential type. Let A be its one-dimensional perturbation. We establish necessity of Muckenhoupt condition (A2) for two weights related to operator A for…

We begin an investigation into extending the T1 theorem of David and Journ\'e, and the corresponding cancellation conditions of Stein, to more general pairs of distinct doubling weights. For example, assuming the measures satisfy a…

The purpose of this paper is to consider the minimization problem of the following nonlocal interaction functional \begin{equation*} E[\rho]=\frac{1}{2}\int_{\mathbb{R}^N}…