Improved iterative oscillation tests for first-order deviating differential equations

Abstract

Abstract. In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing lim sup and lim inf on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.

Sufficient oscillation conditions for deviating difference equations

“…then all solutions of (E ) are oscillatory. Several improvements were made to the above conditions, see [4,5,6,10,11] to arrive at the recent forms [6] lim sup…”

Oscillation in deviating differential equations using an iterative method

“…with q 0 (t) = q(t), then all solutions of (2) oscillate. Several improvements were made to above conditions, see [4], [5], [6] to arrive at the recent form [5]…”

“…The problem of establishing sufficient conditions for the oscillation of all solutions of equations (1) and (2) has been the subject of many investigations. The reader is referred to [1], [2], [3], [4], [5], [6], [7], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [20], [21], [22], [23], [24], [25] and the references cited therein. Most of these papers, however, concern the special case where the arguments are nondecreasing.…”

“…Some of these papers study the general case where the arguments are not necessarily monotone. See, for example, [1], [2], [3], [4], [5], [6], [7], [15], [21] and the references cited therein.…”

Oscillation tests for first-order linear differential equations with non-monotone delays

“…In a series of papers, Chatzarakis et al obtained many oscillatory results for Eq. 1, see [5][6][7][8][9][10][11][12][13][14][15]. For example, Chatzarakis [5] improved (5) with n = 3, and (6), and obtained the oscillatory condition…”