We review evolutionary models on quantum graphs expressed by linear and nonlinear
partial differential equations. Existence and stability of the standing waves trapped on …

We compare ground states for the nonlinear Schrödinger equation on metric graphs, defined
as global minimizers of the action functional constrained on the Nehari manifold, and least …

We investigate existence and nonexistence of action ground states and nodal action ground
states for the nonlinear Schr\" odinger equation on noncompact metric graphs with rather …

We construct and quantify asymptotically in the limit of large mass a variety of edge-localized
stationary states of the focusing nonlinear Schrödinger equation on a quantum graph. The …

Given $\lambda> 0$ and $ p> 2$, we present a complete classification of the positive $ H^
1$-solutions of the equation $-u''+\lambda u=| u|^{p-2} u $ on the $\mathcal {T} $-metric …

We investigate the existence of normalized ground states for Schrödinger equations on
noncompact metric graphs in presence of nonlinear point defects, described by nonlinear δ …

We consider the problem of uniqueness of ground states of prescribed mass for the
Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We …

We introduce and implement a method to compute stationary states of nonlinear
Schrödinger equations on metric graphs. Stationary states are obtained as local minimizers …

We establish existence and multiplicity of one-peaked and multi-peaked positive bound
states for nonlinear Schrödinger equations on general compact and noncompact metric …

We study the nonlinear Schrödinger equation with δ s′ coupling of intensity β∈ R∖{0} on
the star graph Γ consisting of N half-lines. The nonlinearity has the form g (u)=| u| p− 1 u, p> …