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 -