Essentially Nonlinear Finite Dimensional Systems

Abstract

This chapter is devoted to systems without linear leading parts. In Section 7.1, the freezing method for linear systems is extended to nonlinear systems having the Lipschitz property. In Section 7.2 we consider nonlinear systems with differentiable right parts. In Section 7.3 we derive solution estimates which generalize the Lozinskii and Wazewski inequalities Nonlinear systems with linear majorants are discussed in Section 7.4. Section 7.5 is devoted to nonlinear triangular systems. Perturbations of general nonlinear systems are investigated in Section 7.6. In Section 7.7 we investigate the asymptotic stability of systems which are ”close” to triangular ones. Nonlinear scalar equations with real variable characteristic roots are examined in Section 7.8.