Oscillation criterion for combined conditionally oscillatory linear differential equations

We analyze second-order linear differential equations whose coefficients contain a power of the independent variable and a general power of the natural logarithm of the independent variable together with periodic (or more general) functions. Such equations are a combination of known types of conditionally oscillatory linear equations. Applying the Riccati transformation and a new modification of the adapted Prüfer angle, we prove an oscillation criterion for the studied equations which is new for several simple linear equations. The novelty is illustrated in examples of such equations.