Existence and regularity of periodic solutions for neutral evolution equations with delays

Abstract

The aim is to study the periodic solution problem for neutral evolution equa-in Banach space X, where A : D(A) ⊂ X → X is a closed linear operator, and −A generates a compact analytic operator semigroup T (t)(t ≥ 0). With the aid of the analytic operator semigroup theories and some fixed point theorems, we obtain the existence and uniqueness of periodic mild solution for neutral evolution equations. The regularity of periodic mild solution for evolution equation with delay is studied, and some the existence results of the classical and strong solutions are obtained. In the end, we give an example to illustrate the applicability of abstract results. Our works greatly improve and generalize the relevant results of existing literatures.

Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line

“…Many works have been devoted to neutral functional differential equations both denselly defined and non-denselly defined conditions of the linear part A. More specifically, when A is the infinitesimal generator of a strongly continuous semigroup on E, we refer to [31], while when A is a Hille-Yosida operator, we refer to [1,3,27].…”

Regularity for Semilinear Neutral Hyperbolic Equations with Cosine Families

“…The nonlinear mapping g : [0, T] × X → X will be explained in detail in Section 3. Semilinear neutral differential equations have been considered by many authors [1,2] and reference therein. We refer to [3,4] for partial neutral integro-differential equations.…”

“…In this paper, we take an approach different to that of previous works (see [2,[19][20][21]) to discuss some kind of solutions of Cauchy initial problems. By means of L 2 -regularity results, we obtain global existence of semilinear neutral hyperbolic equations under more general hypotheses of nonlinear terms.…”