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

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.Comment: We are grateful for any feedback or comment

A fractional Laplacian problem with mixed singular nonlinearities and nonregular data

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.Comment: We are grateful for any feedback or comments. arXiv admin note: text overlap with arXiv:1910.0471

Nonlocal Lazer-McKenna type problem perturbed by the Hardy's potential and its parabolic equivalence

In this paper, we study the effect of Hardy potential on the existence or non-existence of solutions to a fractional Laplacian problem involving a singular nonlinearity. Also, we mention a stability result.Comment: arXiv admin note: text overlap with arXiv:1412.8159 by other author