Multiple solutions for higher-order difference equations

R. P. Agarwal; D. O'Regan

doi:10.1016/S0898-1221(99)00112-1

Multiple solutions for higher-order difference equations

R. P. Agarwal
, D. O'Regan

Mathematics

National University of Singapore

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

18 Citations (Scopus)

Abstract

The n^th (n≥2) order discrete conjugate problem (-1)^n-pΔⁿy(k) = f(k,y(k)), k∈I₀, Δⁱy(0) = 0, 0≤i≤p-1 (here 1≤p≤n-1), Δⁱ(T+n-i) = 0, 0≤i≤n-p-1, and the n^th (n≥2) order discrete (n,p) problem Δⁿy(k)+f(k,y(k)) = 0, k∈I₀, Δⁱy(0) = 0, 0≤i≤n-2, Δ^py(T+n-p) = 0, 0≤p≤n-1 is fixed, are discussed. Let T∈{1,2, ... }, I₀ = {0,1, ..., T}, and y:I_n = {0,1, ..., T+n}→R. Let C(I_n) denote the class of maps w continuous on I_n (discrete topology) with norm |m|₀ = max_i∈I(n) |w(i)|.

Original language	English
Pages (from-to)	39-48
Number of pages	10
Journal	Computers and Mathematics with Applications
Volume	37
Issue number	9
DOIs	https://doi.org/10.1016/S0898-1221(99)00112-1
Publication status	Published - May 1999

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10.1016/S0898-1221(99)00112-1

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@article{ab6e6d6f1873454cb1cd9e4e39221a47,

title = "Multiple solutions for higher-order difference equations",

abstract = "The nth (n≥2) order discrete conjugate problem (-1)n-pΔny(k) = f(k,y(k)), k∈I0, Δiy(0) = 0, 0≤i≤p-1 (here 1≤p≤n-1), Δi(T+n-i) = 0, 0≤i≤n-p-1, and the nth (n≥2) order discrete (n,p) problem Δny(k)+f(k,y(k)) = 0, k∈I0, Δiy(0) = 0, 0≤i≤n-2, Δpy(T+n-p) = 0, 0≤p≤n-1 is fixed, are discussed. Let T∈\{1,2, ... \}, I0 = \{0,1, ..., T\}, and y:In = \{0,1, ..., T+n\}→R. Let C(In) denote the class of maps w continuous on In (discrete topology) with norm |m|0 = maxi∈I(n) |w(i)|.",

author = "Agarwal, \{R. P.\} and D. O'Regan",

year = "1999",

month = may,

doi = "10.1016/S0898-1221(99)00112-1",

language = "English",

volume = "37",

pages = "39--48",

journal = "Computers and Mathematics with Applications",

issn = "0898-1221",

publisher = "Elsevier Ltd",

number = "9",

}

TY - JOUR

T1 - Multiple solutions for higher-order difference equations

AU - Agarwal, R. P.

AU - O'Regan, D.

PY - 1999/5

Y1 - 1999/5

N2 - The nth (n≥2) order discrete conjugate problem (-1)n-pΔny(k) = f(k,y(k)), k∈I0, Δiy(0) = 0, 0≤i≤p-1 (here 1≤p≤n-1), Δi(T+n-i) = 0, 0≤i≤n-p-1, and the nth (n≥2) order discrete (n,p) problem Δny(k)+f(k,y(k)) = 0, k∈I0, Δiy(0) = 0, 0≤i≤n-2, Δpy(T+n-p) = 0, 0≤p≤n-1 is fixed, are discussed. Let T∈{1,2, ... }, I0 = {0,1, ..., T}, and y:In = {0,1, ..., T+n}→R. Let C(In) denote the class of maps w continuous on In (discrete topology) with norm |m|0 = maxi∈I(n) |w(i)|.

AB - The nth (n≥2) order discrete conjugate problem (-1)n-pΔny(k) = f(k,y(k)), k∈I0, Δiy(0) = 0, 0≤i≤p-1 (here 1≤p≤n-1), Δi(T+n-i) = 0, 0≤i≤n-p-1, and the nth (n≥2) order discrete (n,p) problem Δny(k)+f(k,y(k)) = 0, k∈I0, Δiy(0) = 0, 0≤i≤n-2, Δpy(T+n-p) = 0, 0≤p≤n-1 is fixed, are discussed. Let T∈{1,2, ... }, I0 = {0,1, ..., T}, and y:In = {0,1, ..., T+n}→R. Let C(In) denote the class of maps w continuous on In (discrete topology) with norm |m|0 = maxi∈I(n) |w(i)|.

UR - https://www.scopus.com/pages/publications/0033131620

U2 - 10.1016/S0898-1221(99)00112-1

DO - 10.1016/S0898-1221(99)00112-1

M3 - Article

SN - 0898-1221

VL - 37

SP - 39

EP - 48

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9

ER -

Multiple solutions for higher-order difference equations

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