Abstract
We study the following fractional Navier boundary value problem:
{D-alpha(D(beta)u)(x) + u(x)f(x, u(x))=0, 0 < x <1,
lim(x -> 0+) D beta-1 u(x)=0, lim(x -> 0+) D alpha-1 (D(beta)u)(x) = xi,
u(1) = 0, D-beta u(1) = -zeta,
where alpha, beta epsilon (1, 2], D-alpha and D(beta)stand for the standard Riemann-Liouville fractional derivatives, and xi,zeta >= 0 are such that xi + zeta > 0.
Our purpose is to prove the existence, uniqueness, and global asymptotic behavior of a positive continuous solution, where f : (0, 1) x[0, infinity) -> [0, infinity) is continuous and dominated by a function p satisfying appropriate integrability condition.