Stability Criteria For Certain Delay Functional Differential Equations

In this thesis , we first study the stability of the zero solution of the equation x"(t) + p(t)x'(t) + d(t)x'(t-Ï„) + q(t)x(t) + c(t)x(t-Ï„)=0. By using a vector we transfer the second order equation into a first order matric one, then replace the retarded part to be an integral form with a certain equation. After that, in order to transfer the first differential form to a general one we let the vector be another one. Finally, making use of the second Lyapunov method and a Razumikhin-type theorem in a wider way ,we obtain the conditions which ensure the zero solution is uniformly stable, equiasymptotically stable and uniformly asymptotically stable of the certain equation. We also study the stability of the zero solution of the equation with special coefficients.Secondly, we study the oscillation of some equations. By using the differential inequality and the functional sequence, we obtain the sufficient condition which ensures that the equation (r(t)x'(t))' +(?)p_i(t)x(q_i(t))=0 is oscillatory; and we have that the solution of the equation is neither eventually positive nor eventually negative by the differential inequality, then we obtain the sufficient condition of the bounded solutions of the equations (r(t)y'(t))'-a(t)y(t) -(?)[p_i~2+q_i(t)]y(t-Ï„_i)=0 and (r(t)y'(t))'- a(t)y(t) -(?)p_i~2(t)y(t-Ï„_i) = 0 are oscillatory.WANG Jinfeng (Applied mathematics)Supervised by GAO Guozhu...