arXiv subjects

Sedef Karakılıç

Publications and source records attributed to Sedef Karakılıç.

2 recordsLinked to original sources

arXiv2025

On the existence of Nehari ground states for the Nonlinear Schrödinger Equation on Discrete Graphs

We study standing waves for the nonlinear Schrödinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schrödinger operators conditions related with the geometry of the graph that guarantee discreteness of the spectrum and study ground states on the generalized Nehari manifold in order to prove the existence of standing wave solutions in the self-focusing and defocusing case. In this context, we show properties of the solutions, such as integrability. Finally, we discuss decay properties of solutions and the bifurcation of solutions from the trivial solution.

math.AP↗

arXiv2015

Asymptotic Behaviour of Resonance Eigenvalues of the Schrödinger operator with a Matrix Potential

We will discuss the asymptotic behaviour of the eigenvalues of Schrödinger operator with a matrix potential defined by Neumann boundary condition in $L_2^m(F)$, where $F$ is $d$-dimensional rectangle and the potential is a $m \times m$ matrix with $m\geq 2$, $d\geq 2$ , when the eigenvalues belong to the resonance domain, roughly speaking they lie near planes of diffraction. \textbf{Keywords:} Schrödinger operator, Neumann condition, Resonance eigenvalue, Perturbation theory. \textbf{AMS Subject Classifications:} 47F05, 35P15

math.SP↗