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  • On generalized Bregman nonspreading mappings and zero points of maximal monotone operator in a reflexive Banach space
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Lateef Olakunle Jolaoso; Oluwatosin Temitope Mewomo

    The purpose of this paper is to investigate the existence and approximation of fixed points of generalized Bregman nonspreading mapping which are also the zero points of maximal monotone operator in a real reflexive Banach space. Without assuming the ‘AKTT’ condition, we prove a strong convergence theorem for approximating a common element in the set of fixed points of system of generalized Bregman

    更新日期:2020-07-20
  • Some existence results for a quasilinear problem with source term in Zygmund-space
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Boussad Hamour

    In this paper we study the existence of solution to the problem \begin{equation*} \left\{\begin{array}{l} u\in H_{0}^{1}(\Omega), \\ -\textrm{div}\,(A(x)Du)=H(x,u,Du)+f(x)+a_{0}(x)\, u\quad \text{in} \quad\mathcal{D}'(\Omega), \end{array} \right. \end{equation*} where $\Omega$ is an open bounded set of $\mathbb{R}^{2}$, $A(x)$ a coercive matrix with coefficients in $L^\infty(\Omega)$, $H(x,s,\xi)$

    更新日期:2020-07-20
  • A fast method for solving a block tridiagonal quasi-Toeplitz linear system
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Skander Belhaj; Fahd Hcini; Yulin Zhang

    This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block $LU$ decomposition method and

    更新日期:2020-07-20
  • Stein–Weiss inequalities for radial local Morrey spaces
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Kwok-Pun Ho

    This paper establishes a generalization of the celebrated Stein–Weiss inequalities for the fractional integral operators on radial functions in local Morrey spaces. We find that some conditions can be relaxed for the Stein–Weiss inequalities on radial local Morrey spaces.

    更新日期:2020-07-20
  • On the Hilbert vector of the Jacobian module of a plane curve
    Port. Math. (IF 0.517) Pub Date : 2020-06-30
    Armando Cerminara; Alexandru Dimca; Giovanna Ilardi

    We identify several classes of complex projective plane curves $C:f=0$, for which the Hilbert vector of the Jacobian module $N(f)$ can be completely determined, namely the 3-syzygy curves, the maximal Tjurina curves and the nodal curves, having only rational irreducible components. A result due to Hartshorne, on the cohomology of some rank 2 vector bundles on $\mathbb P^2$, is used to get a sharp lower

    更新日期:2020-07-20
  • On a local systolic inequality for odd-symplectic forms
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Gabriele Benedetti; Jungsoo Kang

    The aim of this paper is to formulate a local systolic inequality for odd-symplectic forms (also known as Hamiltonian structures) and to establish it in some basic cases. Let $\Omega$ be an odd-symplectic form on an oriented closed manifold $\Sigma$ of odd dimension. We say that $\Omega$ is Zoll if the trajectories of the flow given by $\Omega$ are the orbits of a free $S^1$-action. After defining

    更新日期:2020-07-20
  • Remarks on the Bohnenblust–Hille inequalities
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Djair Paulino; Daniel Pellegrino; Joedson Santos

    We revisit the Bohnenblust–Hille multilinear and polynomial inequalities and prove some new properties. Our main result is a multilinear version of a recent result on polynomials whose monomials have a uniformly bounded number of variables.

    更新日期:2020-07-20
  • The impact of a lower order term in a Dirichlet problem with a singular nonlinearity
    Port. Math. (IF 0.517) Pub Date : 2020-07-15
    Lucio Boccardo; Gisella Croce

    In this paper we study the existence and regularity of solutions to the following Dirichlet problem $$\begin{cases} -\div(a(x)|\nabla u|^{p-2} \nabla u) + u|u|^{r-1} = \dfrac{f(x)}{u^{\theta}} & \mbox{in $\Omega$,} \\ u > 0 & \mbox{in $\Omega$,} \\ u = 0 & \mbox{on $\partial\Omega$} \\ \end{cases}$$ proving that the lower order term $ u|u|^{r-1}$ has some regularizing effects on the solutions.

    更新日期:2020-07-20
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