Normalized solutions for nonlinear Schrödinger equations on graphs

We are concerned with the nonlinear Schrödinger equation with an L2 mass constraint on both finite and locally finite graphs and prove that the equation has a normalized solution by employing variational methods. We also pay attention to the behaviours of the normalized solution as the mass constraint tends to 0+ or +∞ and give clear descriptions of the limit equations. Finally, we provide some numerical experiments on a finite graph to illustrate our theoretical results.