Nontrivial solutions in abstract cones for Hammerstein integral systems

Daniel Franco; Gennaro Infante; Donal O'Regan

Nontrivial solutions in abstract cones for Hammerstein integral systems

Daniel Franco
, Gennaro Infante
, Donal O'Regan

Mathematics

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

37 Citations (Scopus)

Abstract

We establish new criteria for the existence of nonzero solutions of systems of integral equations of the form u_i(t) = B_i (∫_η^μ f_i(s, u_l (s), . . . , u_n (s)) ds) + ∫₀¹ k_i(t, s)f_i(s, u_l (s), . . . , u_n (s)) ds, where B_i are continuous functions, [η, μ] ⊂ [0, 1], f _i satisfy Carathéodory conditions and k_i may be discontinuous and change sign. We apply our results to prove the existence of nontrivial solutions of some systems of differential equations with nonlinear boundary conditions.

Original language	English
Pages (from-to)	837-850
Number of pages	14
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume	14
Issue number	6
Publication status	Published - Dec 2007

Keywords

Cone
Fixed point index
Nonzero solution

Cite this

@article{ab278849ac224d49bbbd766ee7868ede,

title = "Nontrivial solutions in abstract cones for Hammerstein integral systems",

abstract = "We establish new criteria for the existence of nonzero solutions of systems of integral equations of the form ui(t) = Bi (∫ημ fi(s, ul (s), . . . , un (s)) ds) + ∫01 ki(t, s)fi(s, ul (s), . . . , un (s)) ds, where Bi are continuous functions, [η, μ] ⊂ [0, 1], f i satisfy Carath{\'e}odory conditions and ki may be discontinuous and change sign. We apply our results to prove the existence of nontrivial solutions of some systems of differential equations with nonlinear boundary conditions.",

keywords = "Cone, Fixed point index, Nonzero solution",

author = "Daniel Franco and Gennaro Infante and Donal O'Regan",

year = "2007",

month = dec,

language = "English",

volume = "14",

pages = "837--850",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis",

issn = "1201-3390",

publisher = "Watam Press",

number = "6",

}

TY - JOUR

T1 - Nontrivial solutions in abstract cones for Hammerstein integral systems

AU - Franco, Daniel

AU - Infante, Gennaro

AU - O'Regan, Donal

PY - 2007/12

Y1 - 2007/12

N2 - We establish new criteria for the existence of nonzero solutions of systems of integral equations of the form ui(t) = Bi (∫ημ fi(s, ul (s), . . . , un (s)) ds) + ∫01 ki(t, s)fi(s, ul (s), . . . , un (s)) ds, where Bi are continuous functions, [η, μ] ⊂ [0, 1], f i satisfy Carathéodory conditions and ki may be discontinuous and change sign. We apply our results to prove the existence of nontrivial solutions of some systems of differential equations with nonlinear boundary conditions.

AB - We establish new criteria for the existence of nonzero solutions of systems of integral equations of the form ui(t) = Bi (∫ημ fi(s, ul (s), . . . , un (s)) ds) + ∫01 ki(t, s)fi(s, ul (s), . . . , un (s)) ds, where Bi are continuous functions, [η, μ] ⊂ [0, 1], f i satisfy Carathéodory conditions and ki may be discontinuous and change sign. We apply our results to prove the existence of nontrivial solutions of some systems of differential equations with nonlinear boundary conditions.

KW - Cone

KW - Fixed point index

KW - Nonzero solution

UR - https://www.scopus.com/pages/publications/37349060321

M3 - Article

AN - SCOPUS:37349060321

SN - 1201-3390

VL - 14

SP - 837

EP - 850

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

IS - 6

ER -

Nontrivial solutions in abstract cones for Hammerstein integral systems

Abstract

Keywords

Other files and links

Fingerprint

Cite this