关于SL问题的第一特征值的下界讨论

A Discussion of the Lower Bound on the First Eigenvalue of Sturm-Liouville Problem

考虑SL问题-y^n+qy=λy,x∈[0,1],边界条件为y(0)=0,(y′(1))/(y(1))=aλ+b,我们得到当q(?)0,a>0,b<1时,上述问题的特征值全大于零.

We consider Sturm- Liouville problem on the interval [0,1] of the form - y＂ ＋ qy = λy, x ∈[0,1 ], with boundary conditions y（0） =0, γ′（1）/γ（1）=aλ＋b. We obtain that all the eigenvalues of the above problem arepositive real numbers when q≥0,a〉0,b〈1.