Normalized Solutions to the mixed fractional Schrodinger equations with potential and general nonlinear term

TL;DR

This paper proves the existence of solutions with prescribed norm for mixed fractional Schrödinger equations involving nonlinear terms, using a novel method that generalizes previous results and applies to various scientific fields.

Contribution

It introduces a new approach to establish solutions with prescribed norm for mixed fractional Schrödinger equations, extending prior work in the field.

Findings

Existence of solutions with prescribed norm established.

Method applicable to a broad class of nonlinear equations.

Results encompass and improve upon previous findings.

Abstract

The purpose of this paper is to establish the existence of solutions with prescribed norm to a class of nonlinear equations involving the mixed fractional Laplacians. This type of equations arises in various fields ranging from biophysics to population dynamics. Due to the importance of these applications, this topic has very recently received an increasing interest. Our method is novel and our results cover all the previous ones.