Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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  • 2020-07-01

    Radii problems for the generalized Mittag-Leffler functions

    Anuja Prajapati

    Abstract : In this paper our aim is to find various radii problems of the generalized Mittag-Leffler function for three different kinds of normalization by using their Hadamard factorization in such a way that the resulting functions are analytic. The basic tool of this study is the Mittag-Leffler function in series. Also we have shown that the obtained radii are the smallest positive roots of some functional equations.

  • 2021-11-01

    Multiplicity of solutions for quasilinear Schr\"{o}dinger type equations with the concave-convex nonlinearities

    In Hyoun Kim, Yun-Ho Kim, Chenshuo Li, Kisoeb Park

    Abstract : We deal with the following elliptic equations: \begin{equation*} \left\{ \begin{array}{ll} \displaystyle -\text{div}(\varphi^{\prime}(|\nabla z|^2)\nabla z) +V(x)|z|^{\alpha-2}z=\lambda \rho(x)|z|^{r-2}z + h(x,z), \\ \vspace{-3mm}\\ \displaystyle z(x) \rightarrow 0, \quad \mbox{as} \ |x| \rightarrow \infty, \end{array}\right. \mbox{in} \,\R^N, \end{equation*} where $N \geq 2$, $1 < p < q < N$, $1 < \alpha \leq p^*q^{\prime}/p^{\prime}$, $\alpha < q$, $1 < r < \min\{p,\alpha\}$, $\varphi(t)$ behaves like $t^{q/2}$ for small $t$ and $t^{p/2}$ for large $t$, and $p^{\prime}$ and $q^{\prime}$ the conjugate exponents of $p$ and $q$, respectively. Here, $V:\mathbb R^{N} \to (0,\infty)$ is a potential function and $h:\mathbb R^{N}\times\mathbb R \to \mathbb R$ is a Carath\'eodory function. The present paper is devoted to the existence of at least two distinct non-trivial solutions to quasilinear elliptic problems of Schr\"{o}dinger type, which provides a concave--convex nature to the problem. The primary tools are the well-known mountain pass theorem and a variant of Ekeland's variational principle.

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  • 2021-11-01

    Bergman type operators on some generalized Cartan-Hartogs domains

    Le He, Yanyan Tang, Zhenhan Tu

    Abstract : For $\mu=(\mu_1,\dots,\mu_t)$ ($\mu_j>0$), $\xi=(z_1,\dots,z_t,w)\in \mathbb{C}^{n_1}\times\cdots\times \mathbb{C}^{n_t}\times \mathbb{C}^m$, define $$\Omega(\mu,t)\!=\!\big\{\xi\in\mathbb{B}_{n_1}\times\cdots\times\mathbb{B}_{n_t}\times\mathbb{C}^{m}: \|w\|^2

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  • 2021-07-01

    Uniqueness of topological solutions for the Gudnason model

    Soojung Kim, Youngae Lee

    Abstract : In this paper, we consider the Gudnason model of $\mathcal{N} = 2$ supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

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  • 2021-07-01

    Normal complex symmetric weighted composition operators on the Hardy space

    Hang Zhou, Ze-Hua Zhou

    Abstract : In this paper, we investigate the normal and complex symmetric weighted composition operators $W_{\psi,\varphi}$ on the Hardy space $H^2(\mathbb{D})$. Firstly, we give the explicit conditions of weighted composition operators to be normal and complex symmetric with respect to conjugations $\mathcal{C}_1$ and $\mathcal{C}_2$ on $H^2(\mathbb{D})$, respectively. Moreover, we particularly investigate the weighted composition operators $W_{\psi,\varphi}$ on $H^2(\mathbb{D})$ which are normal and complex symmetric with respect to conjugations $\mathcal{J}$, $\mathcal{C}_1$ and $\mathcal{C}_2$, respectively, when $\varphi$ has an interior fixed point, $\varphi$ is of hyperbolic type or parabolic type.

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  • 2021-05-01

    Corrigendum to ``A dual iterative substructuring method with a small penalty parameter'', [J. Korean Math. Soc. 54 (2017), No. 2, 461--477]

    Chang-Ock Lee, Eun-Hee Park, Jongho Park

    Abstract : In this corrigendum, we offer a correction to~[J. Korean Math. Soc. 54 (2017), No. 2, 461--477]. We construct a counterexample for the strengthened Cauchy--Schwarz inequality used in the original paper. In addition, we provide a new proof for Lemma~5 of the original paper, an estimate for the extremal eigenvalues of the standard unpreconditioned FETI-DP dual operator.

  • 2021-05-01

    Blow-up of solutions for wave equations with strong damping and variable-exponent nonlinearity

    Sun-Hye Park

    Abstract : In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity $$u_{tt}(x,t) - \Delta u (x,t) - \Delta u_t (x,t) = |u(x,t)|^{p(x)-2} u(x,t) , $$ where the exponent $p(\cdot)$ of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

  • 2021-01-01

    Positively expansive maps and the limit shadowing properties

    Kazuhiro Sakai

    Abstract : In this paper, the notion of two-sided limit shadowing property is considered for a positively expansive open map. More precisely, let $f$ be a positively expansive open map of a compact metric space $X$. It is proved that if $f$ is topologically mixing, then it has the two-sided limit shadowing property. As a corollary, we have that if $X$ is connected, then the notions of the two-sided limit shadowing property and the average-shadowing property are equivalent.

  • 2020-11-01

    A $q$-queens problem V. some of our favorite pieces: queens, bishops, rooks, and nightriders

    Seth Chaiken, Christopher R. H. Hanusa, Thomas Zaslavsky

    Abstract : Parts~I--IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope. Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by \Kot. We prove some of \Kot's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.

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  • 2020-11-01

    Cyclotomic quiver Hecke algebras corresponding to minuscule representations

    Euiyong Park

    Abstract : In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

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May, 2022
Vol.59 No.3

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