| In this thesis,we study multiple solutions of quasilinear equation under some weaker Ambrosetti-Rabinowitz conditions.The approaches we used are variational methods,the critical point methods and analytical techniques.Firstly,we consider a type of quasilinear Schr(?)dinger equation with a parameter on nonlinear term.First,we use a change of variables to transform the quasilinear problem into a semilinear one.By using a generalized Ekeland’s variational principle,we determine the precise positive interval of the parameter when the problem possesses at least two nontrivial solutions.Next,we consider a type of quasilinear elliptic equation.The objection of the study is to get the new results of the existence of infinitely many solutions of the problem by weaken the Ambrosetti and Rabinowitz condition.We use perturbation techniques to overcome the lack of symmetry.When the quasilinear problem does’ t have variation structures,we acquire a new way to overcome the lack of compactness.This extends the previous results. |
