Talk by Dr. Setenay Akduman
On August 4th, 2026, Dr. Setenay Akduman (Izmir Democracy University) gave a talk with the title "On the existence of Nehari ground states for the nonlinear Schrödinger equation on discrete graphs" as part of the research seminar Analysis of the FernUniversität in Hagen.
Abstract
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We study standing wave solutions of the nonlinear Schrödinger equation on discrete graphs. After introducing the variational framework, I will discuss geometric conditions on the underlying graph that guarantee the discreteness of the spectrum of the associated Schrödinger operator. These spectral properties allow us to apply the generalized Nehari manifold approach to prove the existence of standing wave solutions in both the self-focusing and defocusing cases. I will also discuss some qualitative properties of the solutions, including integrability, decay behaviour, and bifurcation from the trivial solution.
