Jong-Rak Lee

We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations $$ \textstyle\begin{cases} {-}\operatorname{div}(\varphi(x,\nabla u))+{|u|}^{p-2}u= \lambda f(x,u) &\mbox{in } \Omega,\\ \varphi(x,\nabla u) \frac{\partial u}{\partial n}= \lambda g(x,u) & \mbox{on }\partial\Omega. \end{cases} $$ Here the function $\varphi(x,v)$ is of type $|v|^{p-2}v$ and the functions f, g satisfy a Carathéodory condition. To do this, we give some critical point theo

Abstract The aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional $p(\cdot )$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> <mml:mo>(</mml:mo> <mml:mo>⋅</mml:mo> <mml:mo>)</mml:mo> </mml:math> -Laplacian with concave–convex nonlinearities when, in general, the nonlinear term does not satisfy the Ambrosetti–Rabinowitz condition. The main tools for obtaining this re

In this paper, we give a characterization of a complex symmetric Toeplitz operator Tφ on the weighted Bergman space Aα2(D). We first give properties of complex symmetric Toeplitz operators Tφ on Aα2(D). Next, we prove that if Tφ is complex symmetric with finite symbol, then Tφ is hyponormal on Aα2(D) if and only if it is hyponormal on the Hardy space H2(T). Finally, we consider the complex symmetric Toeplitz operator Tφ on Aα2(D) when the conjugation is a special case.

&lt;abstract&gt;&lt;p&gt;In this paper we consider the properties of H-Toeplitz operators $ B_{\varphi} $ on the Bergman space $ L^2_a(\Bbb D) $. We present some necessary and sufficient conditions for the contractive and expansive H-Toeplitz operators $ B_\varphi $ with various symbols $ \varphi $.&lt;/p&gt;&lt;/abstract&gt;

In this note we consider the hyponormality of Toeplitz operators <TEX>$T_{\varphi}$</TEX> on the Weighted Bergman space <TEX>$A^2_{\alpha}(\mathbb{D})$</TEX> with symbol in the class of functions <TEX>$f+\bar{g}$</TEX> with polynomials <TEX>$f$</TEX> and <TEX>$g$</TEX> of degree 2.

We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text], [Formula: see text] is the <i>p</i>-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text]. Here, [Formula: see text] is the Riesz potential of order [Formula: see text]. We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solut

Abstract In this paper, we consider the hyponormality of Toeplitz operators acting on the weighted Bergman space $$A_{\alpha }^2({\mathbb{D}}).$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msubsup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>D</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> We establish necessary or sufficient conditions for t

In this paper, we consider the hyponormality of Toeplitz operators Tϕ on the Fock spaces F2. First we characterize the necessary and sufficient conditions for the hyponormality of Toeplitz operators Tϕ on F2 with some symbol ϕ in the class of functions f+g¯ with polynomials f and g. Next, we consider the necessary condition for hyponormality of Tϕ with trigonometric polynomial symbol ϕ.

We are concerned with the following p-biharmonic equations: $$ \Delta _{p}^{2} u+M \biggl( \int _{\mathbb{R}^{N}}\varPhi _{0}(x,\nabla u) \,dx \biggr) \operatorname{div}\bigl(\varphi (x,\nabla u)\bigr)+V(x) \vert u \vert ^{p-2}u=\lambda f(x,u) \quad \text{in } \mathbb{R}^{N}, $$ where $2< 2p<N$ , $\Delta _{p}^{2}u=\Delta (|\Delta u|^{p-2} \Delta u)$ , the function $\varphi (x,v)$ is of type $\lvert v \rvert ^{p-2}v$ , $\varphi (x,v)=\frac{d}{dv}\varPhi _{0}(x,v)$ , the potential function $V:\mat

In this paper, we give a characterization of normality of Toeplitz operator Tφ on the Bergman space A2(D). First, we state basic properties for Toeplitz operator Tφ on A2(D). Next, we consider the normal Toeplitz operator Tφ on A2(D) in terms of harmonic symbols φ. Finally, we characterize the normal Toeplitz operators Tφ with non-harmonic symbols acting on A2(D).