Oscillation of certain fourth-order functional differential equations

Abstract

Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the formare established.

Oscillation of third-order nonlinear functional differential equations with mixed arguments

“…Thus, our method essentially simplifies the examination of the third order equations and what is more, it supports backward the research on the first order delay/advanced differential equations. Our results here extend and complement latest ones of Grace et al [9], Agarwal et al [1]- [3], Cecchi et al [5], Parhi and Pardi [14] and the presents authors [4], [7]. The suitable illustrative examples are also provided.…”

Oscillation criteria for fourth-order functional differential equations

“…Proceeding as in Case (III) of Theorem 2.1, we obtain (2.13) for t ≥ t 4 , and hence, by using (2.13) and (1.5) in (3.10), we get…”

“…Most of the work on this subject, however, has been restricted to first and second-order equations as well as equations of type (1.1) and (1.2) when α = 1 and other higher-order equations. For recent contributions, we refer to [1][2][3][4][5][6][7][8][9][10][11][12]. It appears that little is known regarding the oscillation of equation (1.1) and (1.2).…”

Oscillation Criteria for Certain Fourth-Order Nonlinear Delay Differential Equations

“…Most of the work on this subject, however, has been restricted to firstand second-order equations as well as equations of type (1.1) when α = 1, p(t) = 0 and other higher-order equations. For recent contributions, we refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It appears that little is known regarding the oscillation of Eq.…”