A Kind Of Boundary Value Problem Of Fourth-order Differential Equation

In the fourth-order boundary problemu^（4）+c（x）u=h（x）,u（0）=u（1）=u^’（0）=u^’（1）=0,which describe static elastic beam,the existence of solution is very concerned with c（x）.In this paper,we start with the norm of the related operator,then get the equivalent operator equation of weak solution.Finally,we get the more general existence condition of the solution,prove the related operator is inverse positive and generalize this method to the two-dimensional biharmonic problem.