Existence and regularity of solutions for neutral partial functional integrodifferential 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.…”

Existence results for some neutral functional integrodifferential equations withbounded delay

“…It has been noted that partial functional differential equations with delay have attracted widespread attention in the literature, see for example [2,3,7,[11][12][13][14]20] and the references therein.…”

Existence of solutions for delay evolution equations with nonlocal conditions

“…Since the theory of differential equations with delay has extensive physical background and realistic mathematical model, it has been considerably developed and numerous properties of solutions have been studied, see [14][15][16] and references therein. Therefore, the nonlocal Cauchy problems for evolution equations with delay are an important area of investigation and have been studied extensively in recent years.…”