A fractional Laplacian problem with mixed singular nonlinearities and nonregular data

Abstract

In this note, we study the existence and uniqueness of a positive solution to a doubly singular fractional problem with nonregular data. Besides, for some cases, we will show the existence and uniqueness of another notion of a solution, so-called entropy solution. Also, with suitable assumptions on data, we will discuss the uniqueness. Finally, we will have some relaxation on the assumption to prove the existence results.

We are grateful for any feedback or comments. arXiv admin note: text overlap with arXiv:1910.04716

References in corpus (3)

• Nonlocal equations with measure data
• The Dirichlet problem for the $1$-Laplacian with a general singular term and $L^1$-data
• A note on the existence of a unique positive entropy solution to a fractional Laplacian with singular nonlinearities