Finite many critical problems involving Fractional Laplacians in $\mathbb{R}^{N}$

Yu Su; Haibi Chen

Finite many critical problems involving Fractional Laplacians in $\mathbb{R}^{N}$

Analysis of PDEs 2018-05-29 v2

Authors: Yu Su , Haibi Chen

Abstract

In this paper, we consider the nonlocal elliptic problems in $\mathbb{R}^{N}$ , which involve finite many critical exponents. By using endpoint refined Hardy--Sobolev inequality, fractional Coulomb--Sobolev space and variational method, we establish the existence of nonnegative solution. Our results generalize some results obtained by Yang and Wu [Adv. Nonlinear Stud. (2017) \cite{Yang2017}].

Keywords

nonlocal elliptic problems fractional laplacian critical exponents hardy-sobolev inequality variational method existence of solutions

Cite

@article{arxiv.1805.09150,
  title  = {Finite many critical problems involving Fractional Laplacians in $\mathbb{R}^{N}$},
  author = {Yu Su and Haibi Chen},
  journal= {arXiv preprint arXiv:1805.09150},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1805.08012

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