The non-monotonic ignition response of counterflowing premixed hydrogen/oxygen mixtures with nitrogen dilution versus heated nitrogen is studied numerically and theoretically. It is shown that the three ignition limits can be theoretically obtained by considering only the linear system involving at most only one radical in each reaction, while the influences of the nonlinear reactions, each involving two radicals, together with thermal feedback, introduce higher-order corrections, particularly for the third ignition limit. It is also demonstrated that the high diffusivity of H-2 promotes ignition at the third limit. On the other hand, the high diffusivity of the H atom suppresses ignition at the first limit, while the assumption of unity Lewis number for H yields remarkably good results for the other two limits. Furthermore, by solving the time evolution of the crucial H and HO2 radicals, simplified formulations of the three individual limits and the two quadratic double limits are obtained analytically, in analogy with results for the homogeneous explosion problem. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.