A critical fractional equation with concave convex power nonlinearities Articles uri icon

publication date

  • August 2015

start page

  • 875

end page

  • 900

issue

  • 4

volume

  • 32

International Standard Serial Number (ISSN)

  • 0294-1449

Electronic International Standard Serial Number (EISSN)

  • 1873-1430

abstract

  • In this work we study the following fractional critical problem (P lambda) = {(-Delta)(s)u = lambda u(q+)u(2s)*(-1), u>0 in Omega u=0 in R-n/Omega where Omega subset of R(n)is a regular bounded domain, lambda > 0, 0 2s. Here (-Delta)(S) denotes the fractional Laplace operator defined, up to a normalization factor, by -(-Delta)(S)u(x) = integral u(x+y)+u(x-y)-2u(x)/vertical bar y vertical bar(n+2s) dy, x is an element of R-n. Our main results show the existence and multiplicity of solutions to problem (P-lambda) for different values of lambda. The dependency on this parameter changes according to whether we consider the concave power case (0