一个四阶非线性微分算子的特征值问题

Research on Nonlinear Eigenvalue Problem of A Four Order Ordinary Differential Operater

研究了一个四阶微分算子的非线性特征值问题,首先利用对称全连续算子谱理论得到线性情况下的特征值结果,然后将非线性问题线性化,利用Schauder不动点定理得到一个不动点,而此不动点恰为非线性问题的解,借以证明特征值的存在及相应的估计。

The nonlinear eigenvalue problem of a four order differential operator is researched.The spectrum theory of the symmetrical fully continuous operator can give the result of linear eigenvalue problem.Then,linearizing nonlinear eigenvalue problem and using schauder fixed point theorem,the fixed point of this mapping can be obtained.While,the fixed point is just the solution of the nonlinear eigenvalue problem.The eigenvalue existence is justified.And the correspnding result of nonlinear eigenvalue problem can be obtained by restorting to the linear problem result.