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.

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

References in corpus (12)

• Nonlocal equations with measure data
• Finite and Infinite energy solutions of singular elliptic problems: Existence and Uniqueness
• On singular elliptic equations with measure sources
• Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian
• Existence and localization of solutions for nonlocal fractional equations
• A Lazer-McKenna type problem with measures
• On the Höpf Boundary Lemma for quasilinear problems involving singular nonlinearities and applications
• The fractional Schrödinger equation with singular potential and measure data
• The Dirichlet problem for the $1$-Laplacian with a general singular term and $L^1$-data
• Some remarks on the duality method for Integro-Differential equations with measure data
• Schroedinger operators involving singular potentials and measure data
• A note on the existence of a unique positive entropy solution to a fractional Laplacian with singular nonlinearities