Comparison principles for a class of nonlinear non-local integro-differential operators on unbounded domains

摘要: We present extensions of the comparison and maximum principles available for nonlinear non-local integro-differential operators , of the form on . Here, we consider: unbounded spatial domains , with ; sufficiently regular second order linear parabolic partial differential operators ; sufficiently regular semi-linear terms ; and the non-local term , with in a class of non-negative sufficiently summable kernels. We also provide examples illustrating the limitations and applicability of our results.