Periodic solutions in the α-norm for some neutral partial functional differential equations with finite delay

被引：1

作者：

Ezzinbi K. ^{[1
]}

Kyelem B.A. ^{[2
]}

Ouaro S. ^{[2
]}

机构：

[1] Département de Mathématiques, Université Cadi Ayyad, B.P. 2390, Marrakech

[2] Département de Mathématiques, Université de Ouagadougou, Unité de Formation et de Recherche en Sciences Exactes et Appliquées, B.P. 7021

来源：

Afrika Matematika | 2013年 / 24卷 / 4期

关键词：

Analytic semigroup; Condensing maps; Fixed point theorem; Multivalued maps; Partial functional differential equations of neutral type; Periodic solutions; α-norm;

D O I：

10.1007/s13370-012-0087-5

中图分类号：

学科分类号：

摘要：

The aim of this work is to study the existence of periodic solutions in the α-norm for some partial differential equations of neutral type with finite delay. We assume that the linear part is densely defined and is the generator of an analytic semigroup. The delayed part is assumed to be periodic with respect to the first argument. In nonhomogeneous linear case, we show that the existence of a bounded solution in ℝ+ implies the existence of periodic solution. In nonlinear case, we use two approaches, the first one is based on the ultimate boundedness of the solutions and the second one is based on the multivalued fixed point theory. © 2012 African Mathematical Union and Springer-Verlag.

引用

页码：625 / 645

页数：20

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