Tamkang Journal of Mathematics

On a class of Kirchhoff type problems with singular exponential nonlinearity

Mebarka Sattaf — 2023-04-26

We study the following singular Kirchhoff type problem

\[
\left( P\right) \left\{

\begin{array} [c]{c}

-m\left({\displaystyle\int\limits_{\Omega}}\left\vert \nabla u\right\vert ^{2}dx\right) \Delta u=h\left( u\right)

\frac{e^{\alpha u^{2}}}{\left\vert x\right\vert ^{\beta}}\text{ \ \ \ in} \Omega,\\

u=0 \text{on}\; \partial\Omega

\end{array} \right.

\]

where $\Omega\subset\mathbb{R}^{2}$ is a bounded domain with smooth boundary and $0\in\Omega,$ $\beta\in\left[ 0,2\right)$, $\alpha>0$ and $m$ is a continuous function

on $\mathbb{R}^{+}.$ Here, $h$ is a suitable preturbation of $e^{\alpha u^{2}}$ as $u\rightarrow\infty.$ In this paper, we prove the existence of solutions of

$(P)$. Our tools are Trudinger-Moser inequality with a singular weight and the mountain pass theorem

The evolution of the electric field along optical fiber with respect to the type-2 and 3 PAFs in Minkowski 3-space

Nevin Ertu\u{g} G\"{u}rb\"{u}z — 2023-04-28

In this paper, we introduce the type-2 and the type-3 Positional Adapted Frame(PAF) of spacelike curve and timelike curve in
Minkowski 3-space. From these PAFs, we study the evolutions of the electric field vectors of the type-2 and type-3 PAFs.
As a result, we also investigate the Fermi-Walker parallel and the Lorentz force equation of the electric field vectors for the type-2 and type-3 PAFs in Minkowski 3-space.

Fixed point theorems with PPF dependence in strong partial b-metric spaces

Savita Rathee — 2023-05-03

In this study, PPF dependent fixed point theorems are proved for a nonlinear operator, where the domain space $C[[a, b], E]$ is distinct from the range space, $E$, which is a Strong Partial b-metric space (SPbMS). We obtain existence and uniqueness of PPF dependent fixed point results for the defined mappings under SPbMS. Our results are the extension of fixed point results in SPbMS. Examples are provided in the support of results.

A study of statistical submersions

Aliya Naaz Siddiqui — 2023-05-17

In the sixties, A. Gray \cite{Gr} and B. O'Neill \cite{O1} come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories.

A unique continuation result for a system of nonlinear differential equations

Alex M Montes — 2023-05-22

Using an appropriate Carleman-type estimate, we establish a result of unique continuation for a special class of one-dimensional systems that model the evolution of long water waves with small amplitude in the presence of surface tension.

On the numerical radius of an upper triangular operator matrix

Mehdi Naimi — 2023-07-05

The main purpose of this paper is to give an improvement of numerical radius inequality for an upper triangular operator matrix.