Singular doubly nonlocal elliptic problems with Choquard type critical growth nonlinearities
Analysis of PDEs
2020-02-10 v1
Abstract
The theory of elliptic equations involving singular nonlinearities is well studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we study the very singular and doubly nonlocal singular problem (See below). Firstly, we establish a very weak comparison principle and the optimal Sobolev regularity. Next using the critical point theory of non-smooth analysis and the geometry of the energy functional, we establish the global multiplicity of positive weak solutions.
Cite
@article{arxiv.2002.02937,
title = {Singular doubly nonlocal elliptic problems with Choquard type critical growth nonlinearities},
author = {Jacques Giacomoni and Divya Goel and K. Sreenadh},
journal= {arXiv preprint arXiv:2002.02937},
year = {2020}
}