On implicit abstract neutral nonlinear differential equations (Q282080)

The aim of this work is to study the existence and regularity of solutions for some implicit nonlinear neutral equations with infinite delay. The authors establish the existence of strict solutions. The phase space is axiomatically defined. The linear part is assumed to generate an analytic semigroup. The nonlinear part, where the delay is involved, is assumed to be locally Lipschitz. The authors use the strict contraction principle to prove the main result of this work. For illustration some implicit partial differential equations are provided.