Existence Of Critical Point For Abstract Resonant Problems With Unbounded Nonlinearities And Applications To Differential Equations

In this thesis, using well-known variational methods, we mainly prove a general abstract problem on the existence of critical point for resonant problems with unbounded nonlinearities and then apply it to ordinary and partial differential equations with generalized Ahmad-Lazer-Paul conditions. The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.In the introduction, we briefly introduce the development process of the variational methods. In Chapter 2, we list some basic knowledges refering to the variational methods, including the Sobobev space, —△ operator, the weak solution and the minimizing sequence methods and some minimax theorems. In Chapter 3, we introduce the research process of Hamiltonian system of second order and the semilinear elliptic problems, using the methods introduced previously. In Chapter 4, we prove the main theorem of the thesis, and apply it to the problems in the previous Chapter, and can also be applied to some new resonant cases.