2017
Том 69
№ 9

All Issues

On the Behavior of Solutions of a Third-Order Nonlinear Dynamic Equation on Time Scales

Şenel M. T.

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Abstract

We study oscillatory and asymptotic properties of the third-order nonlinear dynamic equation $$ {{\left[ {{{{\left( {\frac{1}{{{r_2}(t)}}{{{\left( {{{{\left( {\frac{1}{{{r_1}(t)}}{x^{\varDelta }}(t)} \right)}}^{{{\gamma_1}}}}} \right)}}^{\varDelta }}} \right)}}^{{{\gamma_2}}}}} \right]}^{\varDelta }}+f\left( {t,{x^{\sigma }}(t)} \right)=0,\quad t\in \mathbb{T}. $$ By using the Riccati transformation, we present new criteria for the oscillation or certain asymptotic behavior of solutions of this equation. It is supposed that the time scale T is unbounded above.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 7, pp 1111-1121.

Citation Example: Şenel M. T. On the Behavior of Solutions of a Third-Order Nonlinear Dynamic Equation on Time Scales // Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 996–1004.

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