The pseudorelativistic Hartree equation with a general nonlinearity: existence, non existence and variational identities

TL;DR

This paper investigates the existence and non-existence of solitary wave solutions for a class of pseudorelativistic Hartree equations with general nonlinearities, employing variational methods and new identities involving the half Laplacian.

Contribution

It introduces new variational identities involving the half Laplacian and establishes conditions for existence and non-existence of solitary waves in pseudorelativistic Hartree equations.

Findings

Established existence of solitary waves under certain conditions.

Proved non-existence results for specific nonlinearities.

Developed new variational identities involving the half Laplacian.

Abstract

We prove several existence and non existence results of solitary waves for a class of nonlinear pseudo-relativistic Hartree equations with general nonlinearities. We use variational methods and some new variational identities involving the half Laplacian.