TRUDINGER-MOSER TYPE INEQUALITY AND EXISTENCE OF SOLUTION FOR PERTURBED NON-LOCAL ELLIPTIC OPERATORS WITH EXPONENTIAL NONLINEARITY

In this paper we consider the following perturbed nonlocal problem with exponential nonlinearity {-L(K)u + vertical bar u vertical bar(p-2) u + h(u) = f in Omega, u = 0, in R-N \ Omega, (1) where s is an element of (0, 1), N = ps, p >= 2 and f is an element of L-infinity (R-N). First, we generalize a suitable Trudinger-Moser inequality to a fractional functional space. Then, using the Ekeland's variational principle, we prove the existence of a solution of problem (1).