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Existence of multiple solutions for second-order discrete boundary value problems

✍ Scribed by J. Henderson; H.B. Thompson

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
676 KB
Volume
43
Category
Article
ISSN
0898-1221

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✦ Synopsis

we give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem y/k+l -2yk + y/k-l + f(k, yk,uk) = 0, for k = 1,. ,n -I, yo = 0 = y,, where f is continuous and 01, = gk -yk-_l, for k = 1,.

,R. In the special case f(k, t,p) = f(t) 2 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions.

We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue.

πŸ“œ SIMILAR VOLUMES

Existence of multiple solutions for fini
Existence of multiple solutions for finite difference approximations to second-order boundary value problems
✍ H.B. Thompson πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 185 KB

We consider discrete two-point boundary value problems of the form D 2 y k+1 =f(kh; y k ; Dy k ), for k = 1; : : : ; n -1; (0; 0) = G((y0; yn); (Dy1; Dyn)), where Dy k = (y k -y k-1 )=h and h = 1=n. This arises as a ÿnite di erence approximation to y = f(x; y; y ), x ∈ [0; 1], (0; 0) = G((y(0); y(1)

Existence of three positive solutions fo
Existence of three positive solutions for some second-order boundary value problems
✍ Zhanbing Bai; Weigao Ge πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 420 KB

In this paper, a new fixed-point theorem of functional type in a cone is established. With using the new fixed-point theorem and imposing growth conditions on the nonlinearity, the existence of three positive solutions for the boundary value problem x"(O+f(t,x(t),x'(t))=O , 0<t<l, x(0) = x(1) = 0,