Invariance and strict invariance for nonlinear evolution problems with applications

Sufficient conditions for the invariance of evolution problems governed by perturbations (possibly nonlinear) m-accretive operators are provided. The with respect to sublevel sets a constraining functional expressed in terms Dini derivative that functional, outside considered set directions determined operator. An approach non-reflexive Banach spaces is developed and some result improving recent paper (Cannarsa et al., 2018) presented. Applications nonlinear obstacle age-structured population models presented continuous functions where an advantage such taken. Moreover, new abstract criteria so-called strict derived their direct application barriers discussed.