Oscillation of second order mixed functional differential equations with sublinear and superlinear neutral terms

Authors: SHAN SHI, ZHENLAI HAN

Abstract: In this paper, we shall establish some new oscillation theorems for the functional differential equations with sublinear and superlinear neutral terms of the form $$ (r(t)(z'(t))^\alpha)'=q(t)x^\alpha(\tau(t)), $$ where $z(t)=x(t)+p_1(t)x^\beta(\sigma(t))-p_2(t)x^\gamma(\sigma(t))$ with $0<\beta<1$ and $\gamma>1$. Moreover, $\sigma(t)\leq t$ and $\tau(t)$ is a mixed type deviating argument specially. Finally, some relevant examples are indicated to illustrate the applicability of our results.

Keywords: Sublinear and superlinear neutral terms, oscillation, delay, advanced

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