一类特殊双参共振梁方程边值问题解的存在性

Existence Theorem for a Particular Beam Equation Which is Two parameter Reasonant

讨论了一类非线性项比较特殊的双参共振梁方程边值问题，即ｙ（４）＝αｙ－βｙ″＋ｆ（ｙ，ｙ″）＋ｈ（ｘ）ｙ（０）＝ｙ（１）＝ｙ″（０）＝ｙ″（１）＝０｛其中（α，β）为特征值对。利用ｆ（ｙ，ｙ″）在（０，０）处的Ｔａｙｌｏｒ展开，再运用Ｓｃｈａｕｄｅｒ不动点定理，给出了该边值问题的一个存在性结果。

Abstract We discuss a particular beam equation, that is y (4) =αy-βy ″+f(y,y ″)+h(x) y(0)=y(1)=y ″(0)=y ″(1)=0 in which (α,β) is a pair of eigenvalue. Using Taylor Formula for f(y,y ″) in (0,0) and schauder fixed point theorem, we get a existence result.