In this paper we are concerned with the existence of normalized solutions for nonlinear
Schrödinger equations on noncompact metric graphs with localized nonlinearities. In a L 2 …

We present a systematic collection of spectral surgery principles for the Laplacian on a
compact metric graph with any of the usual vertex conditions (natural, Dirichlet, or $\delta …

We study the existence of positive solutions with prescribed L 2-norm for the mass
supercritical Schrödinger equation− Δ u+ λ u− V (x) u=| u| p− 2 uu∈ H 1 (RN), λ∈ R, where …

This open access book gives a systematic introduction into the spectral theory of differential
operators on metric graphs. Main focus is on the fundamental relations between the …

We investigate the relations between normalized critical points of the nonlinear Schrödinger
energy functional and critical points of the corresponding action functional on the associated …

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 prove the existence of solutions (λ, v)∈ R× H 1 (Ω) of the elliptic problem {− Δ v+(V (x)+
λ) v= vp in Ω, v> 0,∫ Ω v 2 dx= ρ. Any v solving such problem (for some λ) is called a …

This paper is devoted to the existence of non-trivial bound states of prescribed mass for the
mass-supercritical nonlinear Schrödinger equation on compact metric graphs. The …

We derive a number of upper and lower bounds for the first nontrivial eigenvalue of
Laplacians on combinatorial and quantum graph in terms of the edge connectivity, ie the …

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 …