Annali di Matematica Pura ed Applicata最新文献

A theory of partial separability for classical Hamiltonian systems is proposed in the context of Haantjes geometry. As a general result, we show that the knowledge of a non-semisimple symplectic-Haantjes manifold for a given Hamiltonian system is sufficient to construct sets of coordinates (called Darboux-Haantjes coordinates) that allow both the partial separability of the associated Hamilton-Jacobi equations and the block-diagonalization of the operators of the corresponding Haantjes algebra. We also introduce a novel class of Hamiltonian systems, characterized by the existence of a generalized Stäckel matrix, which by construction are partially separable. They widely generalize the known families of partially separable Hamiltonian systems. The new systems can be described in terms of semisimple but non-maximal-rank symplectic-Haantjes manifolds.

In this paper, we study the fractional Schrödinger–Poisson system with a general nonlinearity as follows:

where (frac{1}{2}<tle s<1), the potential (lin C(mathbb {R}^{2},mathbb {R}^{+})) and (fin C(mathbb {R},mathbb {R})) does not require the classical (AR)-condition. When (l(x)equiv mu >0) is a parameter, by establishing new estimates for the fractional Laplacian, we find two positive solutions, depending on the range of (mu ). As a result, a positive ground state solution with negative energy exists for the non-autonomous system without any symmetry on l(x). When l(x) is radially symmetric, we show that the symmetry breaking phenomenon can occur, and that a non-radial ground state solution with negative energy exists. Furthermore, under additional assumptions on l(x), three positive solutions are found. The intrinsic differences between the planar SP system and the planar fSP system are analyzed.

In the setting of the thin-shell approximation of the Euler equations in spherical coordinates for oceanic flows with variable density on the spinning Earth, we study a vorticity equation for a pseudo stream function (psi ), whereby the assumption of incompressibility allows us to express the density as a function of (psi ). Via an elliptic comparison argument, we show that, under certain assumptions, the (explicit) solution in the case of zero rate of rotation (i.e., on a fixed sphere) in a bounded region with smooth boundary contained either in the Northern or in the Southern Hemisphere is an approximation, in a suitable sense, of the corresponding solution of the equation with positive rate of rotation in the same region. This provides new insight into the dynamics of ocean gyres.

In this paper, we obtain the Gehring–Hayman type theorem on smoothly bounded pseudoconvex domains of finite type in (mathbb {C}^2). As an application, we provide a quantitative comparison between global and local Kobayashi distances near a boundary point for these domains.

In this paper we show that every connected extremal Kähler submanifold of a complex projective space has a natural extension which is a complete Kähler manifold and admits a holomorphic isometric immersion into the same ambient space. We also give an application to study the scalar curvatures of extremal Hypersurfaces of complex projective spaces.

In this paper we study a class of variable coefficient third order partial differential operators on ({mathbb {R}}^{n+1}), containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of ({mathbb {R}}^{n+1}). A discussion of possible applications in the context of dispersive equations is provided.