On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

Volume 81 / 2003

N. Parhi, R. N. Rath Annales Polonici Mathematici 81 (2003), 101-110 MSC: 34C10, 34C15, 34K40. DOI: 10.4064/ap81-2-1

Abstract

Sufficient conditions are obtained so that every solution of $$ [y(t) - p(t) y(t-\tau )]^{(n)} + Q(t) G (y(t-\sigma )) = f(t) $$ where $n\ge 2$, $p, f\in C([0, \infty ), {{\mathbb R}})$, $Q \in C ([0, \infty ), [0, \infty ))$, $G \in C({{\mathbb R}}, {{\mathbb R}}), \tau > 0$ and $\sigma \ge 0$, oscillates or tends to zero as $t\to \infty $. Various ranges of $p(t)$ are considered. In order to accommodate sublinear cases, it is assumed that $\int _0^{\infty }Q(t)\, dt=\infty $. Through examples it is shown that if the condition on $Q$ is weakened, then there are sublinear equations whose solutions tend to $\pm \infty $ as $t\to \infty $.

Authors

  • N. ParhiDepartment of Mathematics
    Berhampur University
    Berhampur 760007, Orissa, India
    e-mail
  • R. N. RathDepartment of Mathematics
    Khallikote (Autonomous) College
    Berhampur 760001, Orissa, India
    e-mail

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