STUDY OF FRACTIONAL SEMIPOSITONE PROBLEMS ON RN

Let s is an element of (0, 1) and N > 2s. In this paper, we consider the following class of nonlocal semipositone problems: (-Delta)(s) u = g(x) fa(u) in R-N, u > 0 in R-N, where the weight g s L-1( R-N) n L-infinity(R-N) is positive, a > 0 is a parameter, and f(a) is an element of C(R) is strictly negative on (-infinity, 0]. For f(a) having subcritical growth and weaker Ambrosetti-Rabinowitz type nonlinearity, we prove that the above problem admits a mountain pass solution u(a), provided a is near zero. To obtain the positivity of u(a), we establish a Brezis-Kato type uniform estimate of ( u(a)) in L-r(R-N) for every r is an element of [ 2(N) /N-2s, infinity].