Tamkang Journal of Mathematics

Various new traveling wave solutions for conformable time-fractional Sasa-Satsuma equation

2023-08-23T09:11:55+00:00

In this paper, the extended Jacobi elliptic function expansion method is applied to conformable time-fractional Sasa-Satsuma
equation. Variety of new traveling wave solutions are constructed. Thanks to the Mathematica software package, to interprete the behavior of some particular exact solutions, surfaces and contour plots are plotted.

The adjoint map of Euclidean plane curves and curvature problems

2023-10-30T04:30:18+00:00

The adjoint map of a pair of naturally parametrized curves in the Euclidean plane is studied from the point of view of the curvature. A main interest is when the given curve and its adjoint curve share the same natural parameter and the same curvature. For the general linear second order differential equation we introduce a function expressing the deformation of curvatures induced by the adjoint map.

Existence and multiplicity solutions for a singular elliptic p(x)-Laplacian equation

2023-08-23T09:28:24+00:00

This paper deals with the existence and multiplicity of nontrivial weak solutions for the following equation
involving variable exponents:
\begin{align*}
\begin{cases}
-\vartriangle_{p(x)}u+\dfrac{\vert u\vert^{r-2}u}{|x|^{r}}=\lambda h(x,u),&in ~\Omega,\\
u=0,&on~\partial\Omega,
\end{cases}
\end{align*}
where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$ with smooth enough boundary which is subject to Dirichlet boundary condition.
Using a variational method and Krasnoselskii's genus theory, we would show the existence and
multiplicity of the solutions. Next, we study closedness of set of eigenfunctions, such that $p(x)\equiv p$.

A novel iterative algorithm for solving variational inequality, finite family of monotone inclusion and fixed point problems

2023-10-12T04:23:46+00:00

In this paper, we introduce a method for finding common solution of variational inequality, finite family of monotone inclusion and fixed point problems of demicontractive mappings in a real Hilbert space. We prove strong convergence result of proposed method. We also provide a numerical example to show that our method is efficient from the numerical point of view.

Conformal bounds for the first eigenvalue of the $\left(p,q\right)$-Laplacian system

2023-10-02T05:20:07+00:00

Consider $\left(M,g\right)$ as an $m$-dimensional compact connected Riemannian manifold without boundary. In this paper, we investigate the first eigenvalue $\lambda_{1,p,q}$ of the $\left(p,q\right)$-Laplacian system on $M$. Also, in the case of $p,q >n$ we will show that for arbitrary large $\lambda_{1,p,q}$ there exists a Riemannian metric of volume one conformal to the standard metric of $\mathbb{S}^{m}$.

Unique continuation property for the Rosenau equation

2024-01-26T14:43:28+00:00

In this work, using an appropriate Carleman-type estimate, we establish a unique continuation result for the Rosenau equation that models the dynamics of dense discrete systems with high order effects.