Local existence and stability for some partial functional differential equations with infinite delay

Global Attractor for Some Partial Functional Differential Equations with Infinite Delay

“…With regard to the infinite delay case, the situation is di¤erent, since properties of solutions depend on the choice of the phase space. The fundamental theory related to functional di¤erential equations with infinite delay can be found in [25] and we refer the reader to works in [1,2,3,6,10,11,12,13,14,17,24] and the references therein, in which the results are about some quantitative and qualitative aspects of study.…”

“…(1.1), the method of linearization can only be employed to investigate local stability of the equilibria or steady states, see for instance [2,12,17]. Fortunately, if the equation is well-posed, then it may be considered as a dynamical system on some appropriate phase spaces.…”

“…r With regard to equations in the form of Eq. (4.1), we refer to, e.g., [2,37] and their bibliographies, where the existence, regularity and stability of solutions have been studied. Here, we show that, under the above assumptions, Eq.…”

Existence Results for Semilinear Neutral Functional Differential Inclusions via Analytic Semigroups

“…4 we consider a general form of the problem (1,2) where A : D(A) ⊂ E → E is a nondensely defined closed linear operator.…”

“…For this reason, in this paper we discuss existence results for the problem (1,2) in the case where A is a possible unbounded infinitesimal generator of an analytic semigroup of bounded linear operators on E.…”