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We discuss the existence, uniqueness and regularity of solution of abstract neutral differential equations with state-dependent delay. Some examples are presented.

We study the existence and uniqueness of C 1 + α -strict solutions for a general class of abstract differential equations with state dependent delay. We also study the local well-posedness of this type of problems on subspaces of C 1 + α ( [ − p , 0 ] ; X ) . Some examples involving partial differential equations are presented.

In this work we discuss the existence of pseudo S -asymptotically periodic mild solutions for a second order abstract Cauchy problem. In particular, we show that pseudo S -asymptotically ω-periodic cosine functions of operators are ω-periodic. The paper is completed with an application to the nonautonomous wave equation.

In this paper, we study the existence and uniqueness of mild and strict solutions for abstract neutral differential equations with state-dependent delay. In the last section, some examples are presented.

We study the existence and uniqueness of${\mathcal{S}}$-asymptotically periodic solutions for a general class of abstract differential equations with state-dependent delay. Some examples related to problems arising in population dynamics are presented.

In this paper, we study the existence of solutions for a class of abstract fractional non-autonomous differential equations with applications to nonlinear partial differential equations with fractional temporal derivatives. Some examples are presented.

We introduce the concept of pseudo$ \mathcal{S} $-asymptotically periodic functions and study some of the qualitative properties of functions of this type. In addition, we discuss the existence of pseudo$ \mathcal{S} $-asymptotically periodic mild solutions for abstract neutral functional differential equations. Some applications involving ordinary and partial differential equations with delay are presented.

Made available in DSpace on 2018-11-26T15:30:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-08-01 CONICYT DICYT-USACH In this note we study the existence of global solutions for a class of impulsive abstract differential equations with non-instantaneous impulses. Specifically, we establish the existence of mild solutions on and the existence of -asymptotically -periodic mild solutions. Our results are based on the Hausdorff measure of non-compactness. Some applications involving partial differential equations are considered. Univ Sao Paulo, Dept Comp & Matemat, Fac Filosofia Ciencias & Letras Ribeirao Preto, BR-14040901 Ribeirao Preto, SP, Brazil Univ Santiago USACH, Dept Matemat, Casilla 307,Correo 2, Santiago, Chile Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil CONICYT: FONDECYT 1130144

The abstract results and applications presented in “Controllability of fractional neutral stochastic functional differential systems, Z. Angew. Math. Phys. 65 (2014), no. 5, 941–959, are not correct. Moreover, the class of differential control problems studied in [1] is not H-controllable.

Let ( X , ‖ ⋅ ‖ ) be a Banach space and ω ∈ R . A bounded function u ∈ C ( [ 0 , ∞ ) ; X ) is called S -asymptotically ω -periodic if lim t → ∞ [ u ( t + ω ) − u ( t ) ] = 0 . In this paper, we establish conditions under which an S -asymptotically ω -periodic function is asymptotically ω -periodic and we discuss the existence of S -asymptotically ω -periodic and asymptotically ω -periodic solutions for an abstract integral equation. Some applications to partial differential equations and partial integro-differential equations are considered.

We study the existence of asymptotically almost periodic classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations which arise in the study of heat conduction in fading memory material is considered.

Made available in DSpace on 2015-04-27T11:56:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 Made available in DSpace on 2015-04-27T11:56:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 Made available in DSpace on 2015-04-27T11:56:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2011 By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. Universidade Estadual Paulista Júlio de Mesquita Filho, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, Sao Jose do Rio Preto, Rua Cristovão Colombo, 2265, Jardim Nazareth, CEP 15054-000, SP, Brasil Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Matemática, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto

A bounded continuous function $u:[0,\infty )\to X$ is said to be S-asymptotically ω-periodic if $ \lim _{t\to \infty }[ u(t+\omega ) -u(t)]=0$. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.

This paper is devoted to the study of the class of continuous and bounded functions f : [ 0 , ∞ ) → X for which exists ω > 0 such that lim t → ∞ ( f ( t + ω ) − f ( t ) ) = 0 (in the sequel called S-asymptotically ω-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically ω-periodic functions. We also study the existence of S-asymptotically ω-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces.

We introduce a class of abstract differential equation with non instantaneous impulses which extend and generalize some recent models considered in the literature. We study the existence of mild and classical solution and present some applications involving partial differential equations with non-instantaneous impulses.

In this paper, using the theory of analytic semigroup and fractional power of closed operators we study the existence of solutions for a class of semi-linear abstract impulsive differential equations with not instantaneous impulses. Some applications involving partial differential equations with impulses are presented.

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space.

In this paper, we establish the existence of mild solutions for a class of impulsive abstract partial functional differential equation with state-dependent delay.

In [Haiyin Gao, Ke Wang, Fengying Wei, Xiaohua Ding, Massera-type theorem and asymptotically periodic Logistic equations, Nonlinear Analysis: Real World Applications 7 (2006) 1268–1283, Lemma 2.1] it is established that a scalar S -asymptotically ω -periodic function (that is, a continuous and bounded function f : [ 0 , ∞ ) → R such that lim t → ∞ ( f ( t + ω ) − f ( t ) ) = 0 ) is asymptotically ω -periodic. In this note we give two examples to show that this assertion is false.