Asymptotic behaviour and stability of solutions of differential equations

ABSTRACTMaster ThesisASYMPTOTIC BEHAVIOUR AND STABILITY OF SOLUTIONSOF DIFFERENTIAL EQUATIONSSerbay DURANFırat UniversityGraduate School of Natural and Applied SciencesDepartment of Mathematics2006, Page : 48In this study, asymptotic behaviour and stability of the solutions for differentialequations are considered. In the first chapter, some inequalities and fundamental definitions aregiven which are necessary for the remaining chapters of the thesis are presented. In the secondchapter, a fourth order nonlinear wave equation describing the dynamics of a marine riser isconsidered. It is shown that the zero solution of the boundary value problem is globalasymptotic stability. In the third chapter, a partial differential equation describing the dynamicsof a uniform pipe and a system describing the dynamics of a rotating shaft are considered.Sufficient conditions for the global asymptotic stability of the zero solution of the boundaryvalue problem for the differential equation and the differential equation system are establishedby using the Lyapunov function technique.Keywords: Stability, Asymptotic Behaviour, Lyapunov Function.