PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 39(53), pp. 135--147 (1986)
ON ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF A FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATION
D. C. Angelova and D. D. BainovInstitute for social management, Academy of medicine, Sofia
Abstract: Necessary and sufficient conditions for oscillation of solutions of the equation $$ y'(t)+ \gamma f(t,y(t),y(\Delta_1(t,y(t))),\dots, y(\Delta_n(t,y(t))))= Q(t),\enskip t\geq t_0\in R,\enskip \gamma= \pm 1,\enskip n\geq 1 $$ are obtained in the case when $Q(t)\equiv 0$ on $[t_0,\infty)$ and sufficient conditions for oscillation and/or nonoscillation are obtained in the case when $Q(t)\not\equiv 0$ on $[t_0,\infty)$. The asymptotic behaviour of oscillatory and nonoscillatory solutions of this equation is studied, too.
Classification (MSC2000): 34K20
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