Issue 2, Volume 34, August 2009

2009 · Open access

1. NON-EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS IN BOUNDED DOMAINS TRINH THI MINH HANG, HOANG QUOC TOAN PDF

   ▸ Abstract

   In the present paper, by using variational arguments, we prove the non-existence, multiplicity of positive solutions to a system of $p$-Laplace equations of gradient form with nonlinear boundary conditions.

   173-182
2. A LOGARITHMIC QUADRATIC REGULARIZATION METHOD FOR PSEUDOMONOTONE EQUILIBRIUM PROBLEMS PHAM NGOC ANH PDF

   ▸ Abstract

   We use the logarithmic quadratic function to develop two iterative algorithms for solving equilibrium problems. We first use the Bregman distance function to solve a pseudomonotone equilibrium problem satisfying a certain Lipschitz condition. Next, to avoid the Lipschitz condition we combine this technique with line search technique to obtain a convergent algorithm for pseudomonotone equilibrium problems.

   183-200
3. A METHOD OF EXTENDING RANDOM OPERATORS DANG HUNG THANG, TRAN MANH CUONG PDF

   ▸ Abstract

   In this paper, we introduce a method of extending the domain of a random operator to a class of random inputs. This method is based on the convergence of certain random series.

   201-212
4. GLOBAL ATTRACTORS FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS CUNG THE ANH, PHAN QUOC HUNG PDF

   ▸ Abstract

   The aim of this paper is to prove the existence of global solutions and global attractors for a class of semilinear degenerate parabolic equations in an arbitrary domain.

   213-231
5. SHARP INEQUALITY FOR MULTILINEAR COMMUTATOR OF MULTIPLIER OPERATOR KEWEI WANG, LANZHE LIU PDF

   ▸ Abstract

   In this paper, we prove the sharp inequality for multilinear commutator related to the multiplier operators, in which functions belong to BMO space. By using the sharp inequality, we obtain the weighted $L^p$-norm inequality for the multilinear commutator.

   233-244
6. QUASI-CONVEX DUALITY FOR A MIXED 0-1 VARIABLE PROBLEM AND APPLICATIONS IN PRODUCTION PLANNING WITH SET UP COSTS P. T. THACH PDF

   ▸ Abstract

   One of the intractable nonlinear structures comes from the 0-1 variables that formulate, for instance, the discontinuity of set up costs. In this article we consider a mixed 0-1 variable problem that occurs in production planning. By quasi-convex duality we can solve efficiently the problem by linear programs.

   245-256
7. DOMAINS OF OPERATOR SEMI-ATTRACTION OF OPERATOR SEMI-STABLE PROBABILITY MEASURES HO DANG PHUC PDF

   ▸ Abstract

   In this paper we attempt to describe domains of operator semiattraction of operator semi-stable probability measures on finite dimensional Euclidean spaces. We give new characterizations of the operator semi-stability, the domains of operator semi-attraction and the domains of operator attraction.

   257-267
8. ON MINIMAX AND GENERALIZED LOCAL COHOMOLOGY MODULES HERO SAREMI PDF

   ▸ Abstract

   Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring $R$ and $M, N$ be two finitely generated $R$-modules. Let $t$ be a non-negative integer. It is shown that if the local cohomology module $H_{\mathfrak{a}}^i(N)$ is minimax for all $i < t$, then the generalized local cohomology module $H_{\mathfrak{a}}^i(M, N)$ is minimax for all $i < t$. Also, we prove that if the generalized local cohomology module $H^i_{\mathfrak{a}}(M, N)$ is minimax for all i $< t$, then for any minimax module $L$ the $R$-module $\mathrm{Hom}_R(R/\mathfrak{a}, H_{\mathfrak{a}}^t(M, N)/L)$ is finitely generated. In particular, $\mathrm{Ass}_R(H_{\mathfrak{a}}^t(M, N)/L)$ is a finite set.

   269-273
9. RELATIVE CAPACITY AND THE RELATIVE EXTREMAL FUNCTIONS UNDER HOLOMORPHIC COVERINGS LE MAU HAI, TANG VAN LONG PDF

   ▸ Abstract

   In this note we establish formulas on the relative capacity of a subset $E$ in a domain $\Omega \subset \mathbb C^n$ for cases either $\Omega$ is pseudoconvex or $\Omega$ is hyperconvex and $E \subset \Omega$ is a closed subset such that $\overline{E}_{\mathbb C^n} \cap \partial \Omega$ is pluripolar. Moreover the relation between relative extremal functions in a generalized holomorphic covering is studied here.

   275-284
10. A REMARK ON THE KIM’S THEOREM NINH VAN THU PDF

    ▸ Abstract

    In [9], K-T. Kim gave a nice characterization of a domain in $\mathbb C^n$ satisfying the Condition $(L)$ at a boundary point. The key point in his proof is the convergence of the certain scaling sequence. Unfortunately, this assertion is not true. The purpose of this article is twofold. The first is to show a counterexample to the convergence of Kim’s scaling sequence. The second is to give a correct proof of Kim’s characterization theorem.

    285-297