Interval Criteria for Oscillation of Second-Order Linear Ordinary Differential Equations

Abstract

New oscillation criteria are established for the equation py q qy s 0 that are different from most known ones in the sense that they are based on the informaw . tion only on a sequence of subintervals of t , ϱ , rather than on the whole 0 half-line. Our results are more natural according to the Sturm Separation Theorem and sharper than some previous results, and can be applied to extreme cases such ϱ Ž . as H q t dt s yϱ. ᮊ

Oscillation criteria for second order nonlinear neutral differential equations

“…First results of this type were obtained by El-Sayed [3] and later by Huang [7], Kong [9], Li and Agarwal [10], Nasr [12], Sun [16,17], Tiryaki and Zafer [18], and Zheng [22]. These criteria, called interval oscillation theorems, are especially efficient in situations when, for instance, +∞ q(s)ds = −∞, and many advanced oscillation results based on the standard integral averaging technique fail to apply.…”

Interval oscillation criteria for matrix differential systems with damping

“…However, for the scalar equation (2), as implied by the Sturm Separation Theorem, oscillation is essentially an interval property, i.e., if there exists a sequence of subintervals [a i , b i ] of [t 0 , ∞), a i → ∞, such that for each i, there exists a solution of (2) which has at least two zeros in [a i , b i ], then every solution of (2) is oscillatory no matter how "bad" the scalar equation (2)(or (3)) is on the remaining parts of [t 0 , ∞). Based on these facts, Kong [7] gives interval type criteria for the oscillation of system (2), which are extensions of those for scalar equations obtained by Kong [11]. Meanwhile, the oscillation of a system with damping has drawn less attention, Zheng [13] gave oscillation criteria for system (1), which generalize Theorem A.…”

New Oscillation Results for Forced Second Order Differential Equations with Mixed Nonlinearities

“…It has been shown that many real world problems can be modelled, in particular, by half linear differential equations which can be regarded as a natural generalization of linear differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. A considerable amount of research has also been done on quasi-linear [15][16][17][18] and nonlinear second order differential equations [19][20][21][22][23].…”