Uniform dissipative solutions for a certain third order nonlinear differential equation

Abstract

In this paper we study the uniform dissipative solutions for a certain third order nonlinear differential equation. To the best of our knowledge, dissipativity of this class of nonlinear differential equation has never been investigated in the literature. The main aim of this paper is to fill this gap. By employing the frequency domain method and the generalized theorem of Yacubovich on dissipativity, some novel sufficient conditions are obtained to guarantee the existence of uniformly dissipative solutions to the considered equation.