On nonoscillation of advanced differential equations with several terms (Q535978)

Summary: The existence of positive solutions for advanced equations with several terms \[ \dot x(t)+\sum^m_{k=1} a_k(t)x(h_k(t))=0,\quad h_k(t)\geq t \] is investigated in the following three cases: (a) all coefficients \(a_k\) are positive; (b) all coefficients \(a_k\) are negative; (c) there is an equal number of positive and negative coefficients. Results on asymptotics of nonoscillatory solutions are also presented.