Oscillation and non-oscillation of modified Riemann–Weber type equations via comparison theorems

Abstract In this paper, we study the oscillation and non-oscillation of modified Euler type half-linear differential equations with one perturbation in both terms. Such equations are also called the modified Riemann–Weber half-linear equations. Introducing new comparison theorems, we analyse the oscillation behaviour of treated equations, i.e., we enlarge the set of considered equations whose oscillatory properties of solutions are known using the comparison theorems and previously proved oscillation and non-oscillation criteria. Since our results are new even in the intensively studied case of linear equations, we document this novelty by the corresponding new corollaries together with an illustrative example of linear equations whose oscillation and non-oscillation follow from our presented results.