Existence results for nonlinear fractional Dirichlet problems on the right side of the first eigenvalue

Abstract

AbstractIn this paper, we are interested in the study of the existence of solutions of a class of nonlinear fractional differential equations coupled with Dirichlet boundary conditions. We make an exhaustive study of the sign of Green’s function related to the linear problem and obtain the exact values for which it has the constant sign on its whole square of definition. This constant sign is equivalent to the validity of anti-maximum principles. The existence of solutions is deduced from a recent fixed point theorem valid for operators defined on suitable cones of Banach spaces. Moreover, the method of lower and upper solutions is developed for the non-homogeneous Dirichlet problem.