A note on the existence of a unique positive entropy solution to a fractional Laplacian with singular nonlinearities

TL;DR

This paper proves the existence and uniqueness of a positive entropy solution for a fractional Laplacian problem with nonlinear singularities and measure sources, advancing understanding of such complex PDEs.

Contribution

It establishes the first rigorous proof of a unique positive entropy solution in the context of fractional Laplacians with singular nonlinearities and measure data.

Findings

Existence of a positive entropy solution is proven.

Uniqueness of the solution is established.

The solution accommodates measure sources and singular nonlinearities.

Abstract

In this paper, we prove the existence of a unique positive entropy solution to a fractional Laplacian problem involving nonlinear singular terms and also a non-negative bounded Radon measure as a source term.