Oscillation theorems for nonlinear differential equations

J. V. Manojlovic, University of Nis, Nis, Yugoslavia

E. J. Qualitative Theory of Diff. Equ., No. 1. (2000), pp. 1-21.

Abstract: We establish new oscillation theorems for the nonlinear differential equation
$$[a(t)\psi(x(t))|x'(t)|^{\alpha-1}x'(t)]'+q(t)f(x(t))=0, \alpha>0$$
where $a,q:[t0,\infty)\rightarrow R, \psi,f:R\rightarrow R$ are continuous, $a(t)>0$ and $\psi(x)>0$, $xf(x)>0$ for $x\not=0$. These criteria involve the use of averaging functions.

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