On the mild solutions of higher-order differential equations in Banach spaces

Nguyen Thanh Lan
2003 Abstract and Applied Analysis  
For the higher-order abstract differential equationu(n)(t)=Au(t)+f(t),t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspaceℳofBUC(ℝ,E)with respect to the above-mentioned equation in terms of solvability of the operator equationAX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved.
doi:10.1155/s1085337503303057 fatcat:goa56diw2zecpmy5ahpynazhx4