An Ode Approach for Fractional Dirichlet Problems with Gradient Nonlinearity

In the present work we study existence of solutions of fractional Dirichlet problems in the presence of coercive gradient terms with growth comparable and slightly bigger than the order of the nonlocal elliptic operator. We develop a 1-dimensional reduction that allows us to construct barriers via ODE methods and therefore to obtain existence results based on an integral criterion that resembles the classical second-order case. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.