Open AccessELEMENTARY OSCILLATION CRITERIA FOR A THREE TERM RECURRENCE RELATION WITH OSCILLATORY COEFFICIENT SEQUENCE
Author(s) -
Guang Zhang,
Sui-Sun Cheng
Publication year - 1998
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.29.1998.4274
Subject(s) - recurrence relation , mathematics , oscillation (cell signaling) , term (time) , relation (database) , sequence (biology) , pure mathematics , combinatorics , calculus (dental) , discrete mathematics , mathematical analysis , computer science , physics , medicine , data mining , orthodontics , quantum mechanics , genetics , biology
Qualitative properties of recurrence relations with coefficients taking on both positive and negative values are difficult to obtain since mathematical tools are scarce. In this note we start from scratch and obtain a number of oscillation criteria for one such relation : $x_{n+1}-x_n+p_nx_{n-r}\le 0$.