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Zbl 0923.39010
Merdivenci Atici, F.; Guseinov, G.Sh.
Positive periodic solutions for nonlinear difference equations with periodic coefficients.
(English)
[J] J. Math. Anal. Appl. 232, No.1, 166-182 (1999). ISSN 0022-247X

The authors consider the following boundary value problem $$-\Delta [p(n-1)\Delta y(n-1)]+q(n) y(n)=f(n,y(n)), \quad n=1,2,\dots,N,$$ $$y(0)=y(N),\qquad p(0)\Delta y(0)=p(N)\Delta y(N).$$ Using a fixed point theorem in cones, existence of one as well as two solutions is established for the boundary value problem. The authors also consider the boundary value problem with a parameter. Finally, existence of positive periodic solutions on the whole discrete axis is established when the coefficients of the boundary value problem are periodic.
[Patricia J.Y.Wong (Singapore)]
MSC 2000:
*39A12 Discrete version of topics in analysis
39A10 Difference equations

Keywords: nonlinear difference equations; periodic boundary conditions; positive periodic solution; fixed point theorem in cones; periodic coefficients

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