Nonlinear oscillations of second order differential equations of Euler type

We consider the nonlinear equation $t^{2}x'' + g(x) = 0$, where $g(x)$ satisfies $xg(x) > 0$ for $x \ne 0$, but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case $\frac {g(x)}{x} \to \frac {1}{4} \; \text {as} \; |x| \to \infty$, which is most difficult.