Periodic Solutions For Second Order Nonlinear Equations With Singular Vector φ-Laplacian-Like Operators

Second order nonlinear equations withΦ-Laplacian-Like operators is an important model of ordinary differential equations. Attentions are paied to stuuty the periodic solutions of this equation and related problems.The article is giving the continuation lemma on periodic solutions for second or-der nonlinear equations with singular vectorΦ-Laplacian-Like operators, using it proves the existence of T-periodic solutions for second order nonlinear equations with singu-lar vectorΦ-Laplacian-Like operators under Hartman type condition. This work can be viewed as extensions of a series of work about singularΦ-Laplace equations in the respect of higher dimensional system, which was studied by Bereanu and Mawhin recently. Furthermore, we also generalized the averged continuation theoream about periodic solutions for second order nonlinear equations with vectorΦ-Laplacian-Like op-erators which were obtained by Manasevich and Mawhin to singualr vectorΦ-Laplacian-Like operators.