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where a，b，c，d∈（0，∞）， d > c， k = q/p， p， q are positive odd integers， u is a positive integer， pi（m，n），（i = 0，1，2，···u） are positive real sequences.σi，τi∈N0 = {1，2，···}，i = 1，2，···，u. A new comparison theorem for
oscillation of the above equation is obtained.
Key words： Nonlinear partial difference equations； Comparison theorem； Eventually positive solutions
Proof. Suppose， to the contrary， Am，nis an eventually positive solution. From （2.3） aL nedm m（ 2 a.1 28.） 1， fa onrd a anbyo v！e > in 0e，q w uaeli h tya，v ewe Q omb，tnai>n q？！ for m≥M，n≥N. From （2.3），
Proof. Let u∈S. Then from （2.3） and Lemma 2.1， we have？（d？c）+Qm，nAm，n< 0， which implies limm，n→∞supQm，n≤d？c.
This contradicts （2.20）. The proof is complete.
REFERENCES
[1] Yu， J. S.， Zhang， B. G.， & Wang， Z. C. （1994）. Oscillation of delay difference equation. Applicable Analysis， 53， 118-224.
[2] Zhang， B. G.， & Yang， B. （1999）. Oscillation in higher order nonlinear difference equation. Chznese Ann. Math.， 20， 71-80.
[3] Zhou， Y. （2001）. Oscillation of higher-order linear difference equations， advance of diflerence equations III. Special Issue of Computers Math. Application， 42， 323-331.
[4] Lalli， B. S.， & Zhang， B. G. （1992）. On existence of positive solutions and bounded oscillations for neutral difference equations. J. Math. Anal. Appl.， 166， 272-287.
[5] Bohner， M.， & Castillo， J. E. （2001）. Mimetic methods on measure chains. Comput. Math. Appl.， 42， 705-710.
[6] Tanigawa， T. （2003）. Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations. Hiroshima Math.， 33， 297-316.
[7] Bohner， M.， & Peterson， A. （2001）. Dynamic equations on time scales： an tntroduction with applications. Boston： Birkhanser.
[8] Zhang， B. G.， & Zhou， Y. （2001）. Oscillation of a kind of two-variable function equation. Computers and Mathematics with Application， 42， 369-378.
[9] Liu， G. H.， & Liu， L. CH. （2011）. Nonoscillation for system of neutral delay dynamic equation on time scales. Studies in Mathematical Sciences， 3， 16-23.
[10] Zhang， B. G.， & Zhou， Y. （2001）. Oscillation and nonoscillation of second order linear difference equation. Computers Math. Application， 39， 1-7.
oscillation of the above equation is obtained.
Key words： Nonlinear partial difference equations； Comparison theorem； Eventually positive solutions
Proof. Suppose， to the contrary， Am，nis an eventually positive solution. From （2.3） aL nedm m（ 2 a.1 28.） 1， fa onrd a anbyo v！e > in 0e，q w uaeli h tya，v ewe Q omb，tnai>n q？！ for m≥M，n≥N. From （2.3），
Proof. Let u∈S. Then from （2.3） and Lemma 2.1， we have？（d？c）+Qm，nAm，n< 0， which implies limm，n→∞supQm，n≤d？c.
This contradicts （2.20）. The proof is complete.
REFERENCES
[1] Yu， J. S.， Zhang， B. G.， & Wang， Z. C. （1994）. Oscillation of delay difference equation. Applicable Analysis， 53， 118-224.
[2] Zhang， B. G.， & Yang， B. （1999）. Oscillation in higher order nonlinear difference equation. Chznese Ann. Math.， 20， 71-80.
[3] Zhou， Y. （2001）. Oscillation of higher-order linear difference equations， advance of diflerence equations III. Special Issue of Computers Math. Application， 42， 323-331.
[4] Lalli， B. S.， & Zhang， B. G. （1992）. On existence of positive solutions and bounded oscillations for neutral difference equations. J. Math. Anal. Appl.， 166， 272-287.
[5] Bohner， M.， & Castillo， J. E. （2001）. Mimetic methods on measure chains. Comput. Math. Appl.， 42， 705-710.
[6] Tanigawa， T. （2003）. Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations. Hiroshima Math.， 33， 297-316.
[7] Bohner， M.， & Peterson， A. （2001）. Dynamic equations on time scales： an tntroduction with applications. Boston： Birkhanser.
[8] Zhang， B. G.， & Zhou， Y. （2001）. Oscillation of a kind of two-variable function equation. Computers and Mathematics with Application， 42， 369-378.
[9] Liu， G. H.， & Liu， L. CH. （2011）. Nonoscillation for system of neutral delay dynamic equation on time scales. Studies in Mathematical Sciences， 3， 16-23.
[10] Zhang， B. G.， & Zhou， Y. （2001）. Oscillation and nonoscillation of second order linear difference equation. Computers Math. Application， 39， 1-7.