Li¨¦nard Equation Singularity

This dissertation studies the singular points of Lienard equation.The classification and criterion methods for the singular points of 2D linear Lienard equation have been intensively studied. However, there are much less results on the nonlinear systems. Lienard system is a representative of nonlinear systems, but apart from the centers, most studies on the properties of its singular points, such as stability, oscillation, boundedness and the limit circles, are dealt with only the specific problems. Comprehensive analysis and systematic results are rarely found in literature.By analyzing the statues and the distribution of the singular points of the Lienard system, a sufficient condition of discriminating the stability of a singular point is presented in this dissertation. A necessary and sufficient condition is also give. Both of which are not found in literature.The condition for a singular point to be a center is also studied. Though many results of the problem can be found in previous papers, they are under the condition thatwhile F(x) ≠ 0.Where α > 1/4. is constant. In this dissertation, we widen the conditionto α > 0 by adding an additional condition. The existence condition of singular closed orbits of the Lienard system is also discussed.As a specialty of this dissertation, systematic study of the singular points of Lienard equation is given. Some methods are raised in deriving the results such as lemma 4, corollary 3 and corollary 3 etc.