Existence And Multiplicity Of Periodic Solutions For Several Classes Of(q,p)-Laplacian Systems

By using the Least Action Principle, Saddle Point Theorem, Mountain Pass The-orem and Local Linking Theorem, in this doctoral dissertation, the existence and mul-tiplicity of periodic solutions for several class of nonlinear (q, p)-Laplacian ordinary dif-ferential dynamical systems are studied. The dissertation is made up by five chapters.In Chapter1, the historical background of the investigated fields is introduced and the present status of the investigated problems and the main results of this dissertation are summarized.In Chapter2, by using the Least Action Principle and Saddle Point Theorem, the existence and multiplicity of periodic solutions for the following nonautonomous (q,p)-Laplacian dynamical system are studied. Under sub-q and sub-p growth conditions, some new existence results are obtained and these results extend and improve some results in known literature.In Chapter3, by using the Least Action Principle and Local Linking Theorem, the existence and multiplicity of periodic solutions for the following autonomous (q,p)-Laplacian dynamical system with impulsive effects By using those methods and technique in some know literature, some new existence and multiplicity results are obtained.In Chapter4, the existence of periodic solutions for the following nonautonomous (q,p)-Laplacian dynamical system with impulsive effects are studied. By using the Least Action Principle and Mountain Pass Theorem, under sub-min{q,p} and super-max{2,p, q}, some new existence results are obtained.In Chapter5, the existence and multiplicity of periodic solutions for the following damped vibration (q, p)-Laplacian dynamical system and the following damped vibration p-Laplace system By using the Least Action Principle, Saddle Point Theorem and Local Linking Theorem, some new existence results are obtained.