Anti-periodic solutions for evolution equations with mappings in the class (S+)

Yu Qing Chen; Yeol Je Cho; Donal O'Regan

doi:10.1002/mana.200410245

Anti-periodic solutions for evolution equations with mappings in the class (S₊)

Yu Qing Chen, Yeol Je Cho, Donal O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

14 Citations (Scopus)

Abstract

In this paper, we study the existence of anti-periodic solutions for the first order evolution equation {u′(t) + ∂Gu(t) + f(t) = 0, t ∈ ℝ, u(t + T) = -u(t), t ∈ ℝ, in a Hilbert space H, where G : H → ℝ is an even function such that ∂G is a mapping of class (S₊) and f : ℝ → ℝ satisfies f(t + T) = -f(t) for any t ∈ ℝ with f(·) ∈ L² (0, T; H).

Original language	English
Pages (from-to)	356-362
Number of pages	7
Journal	Mathematische Nachrichten
Volume	278
Issue number	4
DOIs	https://doi.org/10.1002/mana.200410245
Publication status	Published - 1 Jan 2005

Keywords

A mapping of class (S )
Anti-periodic solution
Evolution equation

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Chen, YQ;Cho, YJ;O'Regan, D

Access to Document

10.1002/mana.200410245

Cite this

@article{aa5aa38014c444eeba698dc21b8207fb,

title = "Anti-periodic solutions for evolution equations with mappings in the class (S+)",

abstract = "In this paper, we study the existence of anti-periodic solutions for the first order evolution equation {u′(t) + ∂Gu(t) + f(t) = 0, t ∈ ℝ, u(t + T) = -u(t), t ∈ ℝ, in a Hilbert space H, where G : H → ℝ is an even function such that ∂G is a mapping of class (S+) and f : ℝ → ℝ satisfies f(t + T) = -f(t) for any t ∈ ℝ with f(·) ∈ L2 (0, T; H).",

keywords = "A mapping of class (S ), Anti-periodic solution, Evolution equation",

author = "Chen, {Yu Qing} and Cho, {Yeol Je} and Donal O'Regan",

year = "2005",

month = jan,

day = "1",

doi = "10.1002/mana.200410245",

language = "English",

volume = "278",

pages = "356--362",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

number = "4",

}

TY - JOUR

T1 - Anti-periodic solutions for evolution equations with mappings in the class (S+)

AU - Chen, Yu Qing

AU - Cho, Yeol Je

AU - O'Regan, Donal

PY - 2005/1/1

Y1 - 2005/1/1

N2 - In this paper, we study the existence of anti-periodic solutions for the first order evolution equation {u′(t) + ∂Gu(t) + f(t) = 0, t ∈ ℝ, u(t + T) = -u(t), t ∈ ℝ, in a Hilbert space H, where G : H → ℝ is an even function such that ∂G is a mapping of class (S+) and f : ℝ → ℝ satisfies f(t + T) = -f(t) for any t ∈ ℝ with f(·) ∈ L2 (0, T; H).

AB - In this paper, we study the existence of anti-periodic solutions for the first order evolution equation {u′(t) + ∂Gu(t) + f(t) = 0, t ∈ ℝ, u(t + T) = -u(t), t ∈ ℝ, in a Hilbert space H, where G : H → ℝ is an even function such that ∂G is a mapping of class (S+) and f : ℝ → ℝ satisfies f(t + T) = -f(t) for any t ∈ ℝ with f(·) ∈ L2 (0, T; H).

KW - A mapping of class (S )

KW - Anti-periodic solution

KW - Evolution equation

UR - http://www.scopus.com/inward/record.url?scp=15944378572&partnerID=8YFLogxK

U2 - 10.1002/mana.200410245

DO - 10.1002/mana.200410245

M3 - Article

SN - 0025-584X

VL - 278

SP - 356

EP - 362

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 4

ER -