A fundamental problem about polynomials orthogonal on a finite interval is to determine if the linearization coefficients are nonnegative. There have been two ways to do this for specific sets of orthogonal polynomials. One is to find a representation for the coefficients where the nonnegativity is clear. The other is to use the difference equations the linearization coefficients satisfy. The cases where explicit formulas are known are then a challenge to find a general theorem on difference equations which will not only give the known nonnegativity, but then be applicable for many other sets of polynomials where explicit formulas can not be found. The author has found another such general theorem which can be used for some \(q\)-orthogonal polynomials when \(- 1 < q < 0\). Along the way he shows that normalization to 1 at an end point is optimal for appropriate monotonicity conditions on the 3-term recurrence coefficients, and is able to relax monotonicity of full sequences to monotonicity on a pair of sieved sequences with even and odd subscripts. There are further known nonnegative results for sieved ultraspherical polynomials of both the first and second kind, which suggests there are further generalizations to more than a dissection of the integers. The author investigates sufficient conditions for the existence of oscillatory solutions of equations of the form \[ u''' + p_1 (t) u'' + p_2 (t) u'' + p_3 (t)u = 0. \] This interesting survey includes recent results on oscillatory solutions. It is a continuation of the article by \textit{K.-H. Mayer} [J. Oscillation 136, No. 5, 35-102 (1987)].