Constant-sign solutions of a system of volterra integral equations in orlicz spaces

Ravi P. Agarwal; Donal O'Regan; Patricia J.Y. Wong

doi:10.1216/JIE-2008-20-3-337

Constant-sign solutions of a system of volterra integral equations in orlicz spaces

Ravi P. Agarwal
, Donal O'Regan
, Patricia J.Y. Wong

Mathematics

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

12 Citations (Scopus)

Abstract

We consider the following system of Volterra intergral equations uu₁(t) = g_i(t, s)f_i(s, u₁(s), u₂(s), · · ·, u_n(s))ds, a.e. t ∈ [0,T], 1 ≤ i ≤ n. Criteria are offered for the existence of one and more constantsign solutions u = (u1, u2, · · ·, un) of the system in Lp and the Orlicz spaces. We say u is of constant sign if for each 1 ≤ i ≤ n, Θ_iu_i(t) ≥ 0 for a.e. t ∈ [0,T], where Θ_i ∈ {1,-1} is fixed.

Original language	English
Pages (from-to)	337-378
Number of pages	42
Journal	Journal of Integral Equations and Applications
Volume	20
Issue number	3
DOIs	https://doi.org/10.1216/JIE-2008-20-3-337
Publication status	Published - 2008

Keywords

Constant-sign solutions
Orlicz space
System of volterra integral equations

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10.1216/JIE-2008-20-3-337

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title = "Constant-sign solutions of a system of volterra integral equations in orlicz spaces",

abstract = "We consider the following system of Volterra intergral equations uu1(t) = gi(t, s)fi(s, u1(s), u2(s), · · ·, un(s))ds, a.e. t ∈ [0,T], 1 ≤ i ≤ n. Criteria are offered for the existence of one and more constantsign solutions u = (u1, u2, · · ·, un) of the system in Lp and the Orlicz spaces. We say u is of constant sign if for each 1 ≤ i ≤ n, Θiui(t) ≥ 0 for a.e. t ∈ [0,T], where Θi ∈ \{1,-1\} is fixed.",

keywords = "Constant-sign solutions, Orlicz space, System of volterra integral equations",

author = "Agarwal, \{Ravi P.\} and Donal O'Regan and Wong, \{Patricia J.Y.\}",

year = "2008",

doi = "10.1216/JIE-2008-20-3-337",

language = "English",

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journal = "Journal of Integral Equations and Applications",

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TY - JOUR

T1 - Constant-sign solutions of a system of volterra integral equations in orlicz spaces

AU - Agarwal, Ravi P.

AU - O'Regan, Donal

AU - Wong, Patricia J.Y.

PY - 2008

Y1 - 2008

N2 - We consider the following system of Volterra intergral equations uu1(t) = gi(t, s)fi(s, u1(s), u2(s), · · ·, un(s))ds, a.e. t ∈ [0,T], 1 ≤ i ≤ n. Criteria are offered for the existence of one and more constantsign solutions u = (u1, u2, · · ·, un) of the system in Lp and the Orlicz spaces. We say u is of constant sign if for each 1 ≤ i ≤ n, Θiui(t) ≥ 0 for a.e. t ∈ [0,T], where Θi ∈ {1,-1} is fixed.

AB - We consider the following system of Volterra intergral equations uu1(t) = gi(t, s)fi(s, u1(s), u2(s), · · ·, un(s))ds, a.e. t ∈ [0,T], 1 ≤ i ≤ n. Criteria are offered for the existence of one and more constantsign solutions u = (u1, u2, · · ·, un) of the system in Lp and the Orlicz spaces. We say u is of constant sign if for each 1 ≤ i ≤ n, Θiui(t) ≥ 0 for a.e. t ∈ [0,T], where Θi ∈ {1,-1} is fixed.

KW - Constant-sign solutions

KW - Orlicz space

KW - System of volterra integral equations

UR - https://www.scopus.com/pages/publications/80054061306

U2 - 10.1216/JIE-2008-20-3-337

DO - 10.1216/JIE-2008-20-3-337

M3 - Article

SN - 0897-3962

VL - 20

SP - 337

EP - 378

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

IS - 3

ER -

Constant-sign solutions of a system of volterra integral equations in orlicz spaces

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Keywords

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