Existence And Uniqueness Of Solutions For A Nonlinear Fourth-Order Periodic Boundary Value Problem

In this paper,we mainly investigate the existence and uniqueness of solutions in H4(0,2?)for a class of nonlinear fourth-order periodic boundary value problem of the form where g(s)=?s+g(s),g:R?R is continuous,?=m2(m?N),c=am2?a<0,p(·)?L2(0,2?).In the second Chapter,we give some definitions and lemmas as preparatory knowledge to prepare for the main results in the third Chapter.In the third Chapter,we first discuss the necessity of solutions to the above problems,the es-timation of linear part,the prior estimation of solutions and the calculation of degree.Then the existence and uniqueness of the solutions to the above problems are obtained by using the Mawhin's continuity theorem and some analysis techniques.In Chapter 4,two examples are given to illustrate the effectiveness of the our results.