Existence of solutions to singular integral equations

R. P. Agarwal; D. O'Regan

doi:10.13025/23719

Existence of solutions to singular integral equations

R. P. Agarwal
, D. O'Regan

Mathematics

National University of Singapore

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

9 Citations (Scopus)

Abstract

Nonnegative solutions are established for singular integral equations of the form y(t) = h(t)+∫₀^Tk(t,s) f(s,y(s))ds for t∈[0,T]. The linearity f(t,y) may be singular at y = 0. y(t) = ∫₀^Tt^γ√s+t([y(s)]^-α +[y(s)]^β+1)ds, for t∈[0,T], with α>0, 0≤β<1, γ≥0, and γα<1, has a solution y∈C[0,T] with y>0 on [0,T].

Original language	English
Pages (from-to)	25-29
Number of pages	5
Journal	Computers and Mathematics with Applications
Volume	37
Issue number	9
DOIs	https://doi.org/10.13025/23719 https://doi.org/10.1016/s0898-1221(99)00110-8
Publication status	Published - May 1999

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10.13025/23719Licence: CC BY-NC-ND
10.1016/s0898-1221(99)00110-8

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title = "Existence of solutions to singular integral equations",

abstract = "Nonnegative solutions are established for singular integral equations of the form y(t) = h(t)+∫0Tk(t,s) f(s,y(s))ds for t∈[0,T]. The linearity f(t,y) may be singular at y = 0. y(t) = ∫0Ttγ√s+t([y(s)]-α +[y(s)]β+1)ds, for t∈[0,T], with α>0, 0≤β<1, γ≥0, and γα<1, has a solution y∈C[0,T] with y>0 on [0,T].",

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T1 - Existence of solutions to singular integral equations

AU - Agarwal, R. P.

AU - O'Regan, D.

PY - 1999/5

Y1 - 1999/5

N2 - Nonnegative solutions are established for singular integral equations of the form y(t) = h(t)+∫0Tk(t,s) f(s,y(s))ds for t∈[0,T]. The linearity f(t,y) may be singular at y = 0. y(t) = ∫0Ttγ√s+t([y(s)]-α +[y(s)]β+1)ds, for t∈[0,T], with α>0, 0≤β<1, γ≥0, and γα<1, has a solution y∈C[0,T] with y>0 on [0,T].

AB - Nonnegative solutions are established for singular integral equations of the form y(t) = h(t)+∫0Tk(t,s) f(s,y(s))ds for t∈[0,T]. The linearity f(t,y) may be singular at y = 0. y(t) = ∫0Ttγ√s+t([y(s)]-α +[y(s)]β+1)ds, for t∈[0,T], with α>0, 0≤β<1, γ≥0, and γα<1, has a solution y∈C[0,T] with y>0 on [0,T].

UR - http://hdl.handle.net/10379/8768

UR - https://www.scopus.com/pages/publications/0033131607

U2 - 10.13025/23719

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VL - 37

SP - 25

EP - 29

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9

ER -

Existence of solutions to singular integral equations

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