Stability and boundedness of nonautonomous neutral differential equation with delay

Abstract

We consider the nonautonomous neutral differential equation with delay h p(t) q(t) x(t) + b1x(t - r1) 0 0i0 + a(t) x 00(t) + b2x 00(t - r2) +b(t) x 0 (t) + b3x 0 (t - r3) + c(t)f(x(t - s)) = e(t, x, x0 , x 00). Using the method of Lyapunov, we give conditions for the uniform asymptotic stability and uniform boundedness and square integrability of solutions for the considered system. Our theorems generalize and extend some related results known in the literature. Example is given to show our resuls.

Keywords

• uniform ultimate boundedness
• square integrability
• lyapunov functional
• neutral differential equation of third order