Normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities

TL;DR

This paper proves the existence of normalized solutions for $L^2$-supercritical nonlinear Schrödinger equations on noncompact metric graphs with localized nonlinearities, for any prescribed mass, using a versatile approach.

Contribution

It introduces a method to establish normalized solutions in the $L^2$-supercritical regime on noncompact graphs, applicable to more general equations.

Findings

Existence of solutions for any prescribed mass in the supercritical regime.

Applicable approach for broader classes of equations on noncompact graphs.

Advances understanding of nonlinear Schrödinger equations on complex graph structures.

Abstract

In this paper we are concerned with the existence of normalized solutions for nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearities. In a $L^2$-supercritical regime, we obtain the existence of solutions for any prescribed mass. This result is obtained through an approach which could prove successful to treat more general equations on noncompact graphs.