Constant-sign solutions for singular systems of Fredholm integral equations

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

doi:10.1002/mma.1287

Constant-sign solutions for singular systems of Fredholm integral equations

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

Mathematics

Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
Lee Kong Chian School of Medicine/Nanyang Technological University

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

7 Citations (Scopus)

Abstract

We consider the system of Fredholm integral equations u_i(t)= ∫₀^Tg_i(t,s)[H_i(s,u1)(s),u2(s), ⋯,U_n(s))+K_i(s,u1(s),u2(s),⋯,U _n(s))]ds, t∈[0,T], 1≤i≤n where T>0 is fixed and the nonlinearities H_i(t, u₁, u₂,⋯, u _n) can be singular at t=0 and u_j=0 where j∈{1, 2,⋯, n}. Criteria are offered for the existence of constant-sign solutions, i.e. θ_iu_i(t)≥0 for t∈[0, 1] and 1≤i≤n, where θ_i∈{1,-1} is fixed. We also include an example to illustrate the usefulness of the results obtained.

Original language	English
Pages (from-to)	1783-1793
Number of pages	11
Journal	Mathematical Methods in the Applied Sciences
Volume	33
Issue number	15
DOIs	https://doi.org/10.1002/mma.1287
Publication status	Published - 1 Oct 2010

Keywords

constant-sign solutions
singular equations
system of Fredholm integral equations

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

Authors
Agarwal, RP;O'Regan, D;Wong, PJY
Agarwal, RP,O'Regan, D,Wong, PJY

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10.1002/mma.1287

Cite this

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title = "Constant-sign solutions for singular systems of Fredholm integral equations",

abstract = "We consider the system of Fredholm integral equations ui(t)= ∫0Tgi(t,s)[Hi(s,u1)(s),u2(s), ⋯,Un(s))+Ki(s,u1(s),u2(s),⋯,U n(s))]ds, t∈[0,T], 1≤i≤n where T>0 is fixed and the nonlinearities Hi(t, u1, u2,⋯, u n) can be singular at t=0 and uj=0 where j∈\{1, 2,⋯, n\}. Criteria are offered for the existence of constant-sign solutions, i.e. θiui(t)≥0 for t∈[0, 1] and 1≤i≤n, where θi∈\{1,-1\} is fixed. We also include an example to illustrate the usefulness of the results obtained.",

keywords = "constant-sign solutions, singular equations, system of Fredholm integral equations",

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

year = "2010",

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doi = "10.1002/mma.1287",

language = "English",

volume = "33",

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TY - JOUR

T1 - Constant-sign solutions for singular systems of Fredholm integral equations

AU - Agarwal, Ravi P.

AU - O'Regan, Donal

AU - Wong, Patricia J.Y.

PY - 2010/10/1

Y1 - 2010/10/1

N2 - We consider the system of Fredholm integral equations ui(t)= ∫0Tgi(t,s)[Hi(s,u1)(s),u2(s), ⋯,Un(s))+Ki(s,u1(s),u2(s),⋯,U n(s))]ds, t∈[0,T], 1≤i≤n where T>0 is fixed and the nonlinearities Hi(t, u1, u2,⋯, u n) can be singular at t=0 and uj=0 where j∈{1, 2,⋯, n}. Criteria are offered for the existence of constant-sign solutions, i.e. θiui(t)≥0 for t∈[0, 1] and 1≤i≤n, where θi∈{1,-1} is fixed. We also include an example to illustrate the usefulness of the results obtained.

AB - We consider the system of Fredholm integral equations ui(t)= ∫0Tgi(t,s)[Hi(s,u1)(s),u2(s), ⋯,Un(s))+Ki(s,u1(s),u2(s),⋯,U n(s))]ds, t∈[0,T], 1≤i≤n where T>0 is fixed and the nonlinearities Hi(t, u1, u2,⋯, u n) can be singular at t=0 and uj=0 where j∈{1, 2,⋯, n}. Criteria are offered for the existence of constant-sign solutions, i.e. θiui(t)≥0 for t∈[0, 1] and 1≤i≤n, where θi∈{1,-1} is fixed. We also include an example to illustrate the usefulness of the results obtained.

KW - constant-sign solutions

KW - singular equations

KW - system of Fredholm integral equations

UR - https://www.scopus.com/pages/publications/78649427710

U2 - 10.1002/mma.1287

DO - 10.1002/mma.1287

M3 - Article

SN - 0170-4214

VL - 33

SP - 1783

EP - 1793

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 15

ER -

Constant-sign solutions for singular systems of Fredholm integral equations

Abstract

Keywords

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

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