Differential equations with multiple sign changing convolution coefficients

Abstract

For continuous functions [Formula: see text] and [Formula: see text], which are allowed to change sign, we consider the nonlocal differential equation [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] represents the finite convolution of the functions [Formula: see text] and [Formula: see text]. A model case is the equation [Formula: see text] The existence of at least one positive solution to these problems subjected to a variety of boundary conditions is studied. Due to the use of a nonstandard order cone we are able to achieve our results without having to assume that the coefficients [Formula: see text] and [Formula: see text] are strictly positive.