EXISTENCE OF SOLUTIONS FOR A NONHOMOGENEOUS SEMILINEAR FRACTIONAL LAPLACIAN PROBLEMS

In this paper we consider the following fractional problem (1) [ (-Delta)(s)u = lambda u + g(x, u) - h vertical bar u vertical bar(p-1 )u + f, in Omega u = 0, in R-n \textbackslash{} Omega, where Omega is a bounded domain, g is a bounded Caratheodory function in Omega x R, p > 1, h is a nonnegative locally integrable function in Omega which is strictly positive in a set of positive measure, s is an element of (0, 1), (-Delta)(s) is the nonlocal fractional Laplace operator, lambda is an element of R and f is an element of L-2 (Omega). We prove that there exists a solution of problem for every lambda is an element of R and f is an element of L-2(Omega). (AU)