Positive periodic solutions for nonlinear difference equations with periodic coefficients. (English) Zbl 0923.39010

Merdivenci Atici, F.; Guseinov, G. Sh.

J. Math. Anal. Appl. 232, No. 1, 166-182 (1999).

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.

Reviewer: Patricia J.Y.Wong (Singapore)

MSC:

39A12	Discrete version of topics in analysis
39A10	Additive difference equations

Keywords:

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

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