Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

Rok, strany: 2016, 627 - 650

In this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equation $$ R_n^\triangle (t,x(t))+ b(t)|R_{n-1}^\triangle(t,x(t))|^{\gamma-1} R_{n-1}^\triangle(t,x(t))+ q(t)f(|x(\tau(t))|^{\gamma-1}x(\tau(t)))=0 $$ on an arbitrary time scale $\mathbf{T}$ with $\sup\mathbf{T}=\infty$, where $n\geq 2$, $\gamma >0$ is a constant, $\tau:\mathbf{T}\to\mathbf{T}$ with $\tau(t)\leq t$ and $\lim_{t\to\infty}\tau(t)=\infty$ and $$ R_k(t,x(t))= x(t), if k=0, \\ r_k(t)R^\triangle_{k-1}(t,x(t)), if 1\leq k\leq n-1, \\ r_n(t)|R^\triangle_{n-1}(t,x(t))|^{\gamma-1} R^\triangle_{n-1}(t,x(t)), if k= n, $$ with $r_k(t)$ ($1\leq k\leq n$) are positive rd-continuous functions. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

ISO 690:

Wu, X., Sun, T. 2016. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales. In Mathematica Slovaca, vol. 66, no.3, pp. 627-650. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0166

APA:

Wu, X., Sun, T. (2016). Oscillation criteria for higher order nonlinear delay dynamic equations on time scales. Mathematica Slovaca, 66(3), 627-650. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0166