Ground state, bound state, and normalized solutions to semilinear Maxwell and Schr\"odinger equations

TL;DR

This paper investigates the existence of ground and bound states for semilinear Maxwell and Schrödinger equations, including cases with $L^2$-constraints, contributing to the understanding of their solution structures.

Contribution

It provides new results on the existence of various states for semilinear Maxwell and Schrödinger equations, with or without $L^2$-constraints.

Findings

Existence of ground states established.

Multiple bound states identified.

Results applicable to constrained and unconstrained cases.

Abstract

The existence of ground states and (multiple) bound states to semilinear time-independent Maxwell and Schr\"odinger equations, with or without $L^2$-constraints, is investigated.