Nonoscillation of First Order Impulse Differential Equations with DelayU

Oscillation properties of impulse functional-differential equations are studied for equations of the type m ˙x t.s pi t.x tyti t..s0, tgwa, bx, is1 x j.s0, jfwa, bx, x tj.sbjx tjy0., js1, . . . , k, a-t1-t2- ??? -tk-b. The proven test for oscillation generalizes the known ones and allows consideration of the solvability of boundary value problems for the corresponding nonhomogeneous impulse equations. In particular, for the scalar impulse equation ˙x t.qp t.x tyt t..s0, tg w0, `., x j .s0 for j -0, x tj.sbjx tjy0., bj)0, js1, 2, . . . , * The research is supported by the project Giladi of the Israeli Ministry of Science and the Ministry of Absorption, Center for Absorption in Science.