Oscillation of a kind of two-variables functional equation
In this paper, we consider the functional equation of the form aA(x,sigma (y)) + bA(tau (x),y) - cA(tau (x),sigma (y)) + P(x,y)A(tau (k+1)(x),sigma (l+1)(y) = 0, where a, b, c are positive constants, k, I are positive integers, function P : I x I --> R+ = (0, infinity), I subset of (0, infinity) is an unbounded set, tau, sigma : I --> I, tau (x) not equivalent to x, sigma (y) not equivalent to y, and lim(x --> infinity)tau (x) = infinity, lim(y --> infinity) sigma (y) = infinity, x, y is an element of I. Some oscillation criteria of this equation are obtained. (C) 2001 Elsevier Science Ltd. All rights reserved.
oscillation functional equations positive solutions