Conditionally oscillatory linear differential equations with coefficients containing powers of natural logarithm

Abstract

In this paper, we study linear differential equations whose coefficients consist of products of powers of natural logarithm and very general continuous functions. Recently, using the Riccati transformation, we have identified a new type of conditionally oscillatory linear differential equations together with the critical oscillation constant. The studied equations are a generalization of these equations. Applying the modified Prüfer angle, we prove that they remain conditionally oscillatory with the same critical oscillation constant.

Keywords

• linear equation
• differential equation
• conditional oscillation
• non-oscillation
• logarithm