Forced oscillation of second order linear and half-linear difference equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Forced oscillation of second order linear and half-linear difference equations

Authors:	O. Dosly J. R. Graef J. Jaros

Affiliation:	Mathematical Institute, Czech Academy of Sciences, Zizkova 22, CZ--61662 Brno, Czech Republic ; Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403 ; Department of Mathematical Analysis, Comenius University, 842 15 Bratislava, Slovakia

Abstract:	Oscillation properties of solutions of the forced second order linear difference equation $begin{displaymath}Delta (r_{k}Delta x_{k})+c_{k}x_{k+1}=h_{k} end{displaymath}$ are investigated. The authors show that if the forcing term does not oscillate, in some sense, too rapidly, then the oscillation of the unforced equation implies oscillation of the forced equation. Some results illustrating this statement and extensions to the more general half-linear equation $begin{displaymath}Delta left (r_{k}Phi (Delta x_{k})right )+c_{k}Phi (x_... ...k}, quad Phi (s)=vert svert^{alpha -2}s, quad alpha >1, end{displaymath}$ are also given.

Keywords:	Linear difference equation half-linear difference equation variational principle forced oscillation

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