Theorem 3 (See [8]) Let n E Nno and g (n, u, v) be a decreasing function in u and v for anY fixed n. Suppose that for n 2 no, the inequalities Yn+1 < g (n, Yn, Yn-1 < Un+1 hold. Then Yno-1 Uno-1, Yno < Uno implies that Yn < Un, n > no. Consider the scalar kth-order linear difference equation x (n + k) + P1 (n)x (n + k – 1) + ·+ Pk(n)x (n) = 0, (4) where k is a positive integer and p; : Z+ → C for i = 1, - ..., k. Assume that qi = lim p:(n), i = 1, . .. , k, (5) %3D exist in C. Consider the limiting equation of (4): x (n + k) + q1x (n + k – 1) +..+ qkx (n) = 0. (6)
Theorem 3 (See [8]) Let n E Nno and g (n, u, v) be a decreasing function in u and v for anY fixed n. Suppose that for n 2 no, the inequalities Yn+1 < g (n, Yn, Yn-1 < Un+1 hold. Then Yno-1 Uno-1, Yno < Uno implies that Yn < Un, n > no. Consider the scalar kth-order linear difference equation x (n + k) + P1 (n)x (n + k – 1) + ·+ Pk(n)x (n) = 0, (4) where k is a positive integer and p; : Z+ → C for i = 1, - ..., k. Assume that qi = lim p:(n), i = 1, . .. , k, (5) %3D exist in C. Consider the limiting equation of (4): x (n + k) + q1x (n + k – 1) +..+ qkx (n) = 0. (6)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show me the steps of deremine red and inf is here i need evey I need all the details step by step and inf is here
![Theorem 3 (See [8]) Let n E N, and g (n, , v) be a decreasing function in
и аnd v for anу fixed n. Suppose that for n > по, the inequalities
Yn+1 < g (n, Yn, Yn-1
< Un+1
hold. Then
Упо-1 ипо—1,Упо Ипo
implies that
Yn < Un, n 2 no.
Consider the scalar kth-order linear difference equation
т (п + k) + p1(п)х (п + k — 1) +:..+ pi(n)x (п) — 0,
(4)
where k is a positive integer and p; : Z+
→ C for i = 1, ···
,k. Assume that
qi
lim p:(n), i = 1, ... , k,
(5)
exist in C. Consider the limiting equation of (4):
x (n + k) + q1x (n + k – 1) + · + qkx (n) =
= 0.
(6)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff415ac57-ff92-4e25-9045-4869ff575152%2Fdae887f6-7067-4326-a7bc-ad30e4da3efd%2F7llugg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem 3 (See [8]) Let n E N, and g (n, , v) be a decreasing function in
и аnd v for anу fixed n. Suppose that for n > по, the inequalities
Yn+1 < g (n, Yn, Yn-1
< Un+1
hold. Then
Упо-1 ипо—1,Упо Ипo
implies that
Yn < Un, n 2 no.
Consider the scalar kth-order linear difference equation
т (п + k) + p1(п)х (п + k — 1) +:..+ pi(n)x (п) — 0,
(4)
where k is a positive integer and p; : Z+
→ C for i = 1, ···
,k. Assume that
qi
lim p:(n), i = 1, ... , k,
(5)
exist in C. Consider the limiting equation of (4):
x (n + k) + q1x (n + k – 1) + · + qkx (n) =
= 0.
(6)
![[8] A. Bilgin and M.R.S. Kulenovic, Global asymptotic stability for discrete
single species population models, Discrete Dyn. Nat. Soc., 2017 (2017) 1–
15.
[9] E. Bešo, S. Kalabušić, N. Mujić, E. Pilav, Boundedness of solutions and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff415ac57-ff92-4e25-9045-4869ff575152%2Fdae887f6-7067-4326-a7bc-ad30e4da3efd%2Fc63qhnp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[8] A. Bilgin and M.R.S. Kulenovic, Global asymptotic stability for discrete
single species population models, Discrete Dyn. Nat. Soc., 2017 (2017) 1–
15.
[9] E. Bešo, S. Kalabušić, N. Mujić, E. Pilav, Boundedness of solutions and
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
