An oscillation criterion for a forced second order linear differential equation

Abstract

Abstract.The paper is devoted to an oscillation theorem for the second-order forced linear differential equation of the form (p(t)x')' + q{t)x = g(t). The sign of the coefficient q is not definite, and the function g is not necessarily the second derivative of an oscillatory function. The question raised by

New interval oscillation criteria for second-order functional differential equations with nonlinear damping

“…Under assumptions including .i i i / .iv/, authors in [8] generalize the well-known interval criteria obtained in [1] and [20] (which are the earliest oscillation criteria of interval type in the literature) from linear forced second-order differential equations to general type of equations such as (1). Furthermore, authors in [3] have obtained Kamanev type interval oscillation criteria for the same equation under some assumptions including .i i i / .iv/.…”

Interval oscillation criteria for nonlinear impulsive delay differential equations with damping term

“…and established some interval oscillation criteria which developed some known results for the equations without delay in [12,19,21].…”

Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients

“…We remark that the oscillation of the solutions of (1.7) and (1.8) has been studied by many authors, see for instance [8,[14][15][16][17][18][19][20][21][22][23][24], but to the best of our knowledge there is no result in the literature similar to Theorem 1.1 for such nonlinear equations, especially for (1.6).…”