New Oscillation Results for a Nonlinear Generalization of Euler Differential Equation

Abstract

‎‎‎‎In the present work the oscillatory behavior of the solutions of a nonlinear generalization of Euler equation will be considered in which the‎ ‎nonlinearities satisfy the smoothness conditions which guarantee‎ ‎the uniqueness of solutions of initial value problems‎. ‎However‎, ‎no‎ ‎conditions of sub(super)linearity are assumed‎. ‎Some new‎ ‎sufficient conditions are established ensuring oscillation of all‎ ‎solutions of this equation‎. ‎Examples are also provided to illustrate‎ ‎the relevance of the main results‎.

Keywords

• oscillation
• lienard system
• euler equations