Oscillatory behaviour of third order nonlinear differential equations with a nonlinear nonpositive neutral term

Abstract

The authors present some new oscillation criteria for third order nonlinear differential equations with a nonlinear nonpositive neutral term. The results obtained are new and improve known oscillation criteria appearing in the literature even for equations not having a neutral term. Using comparison methods and integral conditions, the authors obtain five new theorems on the oscillatory behaviour of the solutions. Suggestions for future research are included.

Keywords

• oscillation
• third order
• neutral differential equation
• nonlinear nonpositive neutral term