Advances in Nonlinear Analysis
Advances in Nonlinear Analysis
4 years ago

On the existence and multiplicity of solutions to fractional Lane-Emden elliptic systems involving measures

Mousomi Bhakta, Phuoc-Tai Nguyen
We study positive solutions to the fractional Lane-Emden system (−Δ)su=vp+μin Ω(−Δ)sv=uq+νin Ωu=v=0in Ωc=RN∖Ω,(S) where Ω is a C2 bounded domains in ℝN, s ∈ (0, 1), N > 2s, p > 0, q > 0 and μ, ν are positive measures in Ω. We prove the existence of the minimal positive solution of (S) under a smallness condition on the total mass of μ and ν. Furthermore, if p, q ∈ (1,N+sN−s) and 0 ≤ μ, ν ∈ Lr(Ω), for some r > N2s, we show the existence of at least two positive solutions of (S). The novelty lies at the construction of the second solution, which is based on a highly nontrivial adaptation of Linking theorem. We also discuss the regularity of the solutions. Keywords: nonlocal; system; existence; multiplicity; linking theorem; measure data; source terms; positive solution MSC 2010: Primary 35R11; 35J57; 35J50; 35B09; 35R06

Publisher URL: http://www.degruyter.com/view/j/anona.2020.9.issue-1/anona-2020-0060/anona-2020-0060.xml

Open URL: http://www.degruyter.com/downloadpdf/j/anona.2020.9.issue-1/anona-2020-0060/anona-2020-0060.xml

DOI: 10.1515/anona-2020-0060

Open access
You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.