A concave-convex elliptic problem involving the fractional Laplacian Articles uri icon

publication date

  • February 2013

start page

  • 39

end page

  • 71


  • 143


  • 1

International Standard Serial Number (ISSN)

  • 0308-2105

Electronic International Standard Serial Number (EISSN)

  • 1473-7124


  • We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave—convex term. We completely characterize the range of parameters for which solutions of the problem exist and prove a multiplicity result. We also prove an associated trace inequality and some Liouville-type results.