NONLOCAL HENON EQUATION WITH NONLINEARITIES INVOLVING SOBOLEV CRITICAL AND SUPERCRITICAL GROWTH

In this paper, we study the following class of fractional Henon problems involving exponents critical or supercritical {(-Delta)(s) u = lambda vertical bar x vertical bar(mu) u + vertical bar x vertical bar(alpha) vertical bar u vertical bar((p alpha,s)*(+epsilon)-1)u in Omega, u = 0 in R-N / Omega, where p(alpha,s)* = N+2 alpha+2s/N-2s is the critical exponent for a nonlinearity with Henon weight in nonlocal context, epsilon >= 0, Omega is either a ball or an annulus in R-N, s is an element of (0, 1) and mu, alpha > -2s. We used the Emden-Fowler transformation to make the one-dimensional reduction of problems and under appropriate hypotheses on the constant lambda, we prove the existence of at least one non-trivial radial solution for these problems using the concentration compactness principle or Linking Theorem.