首项系数变号的Sturm-Liouville问题的特征值不等式

Inequalities For Eigenvalues For Sturm-Liouville Problems With Change Sign Leading Coefficient

对于首项系数函数改变符号的Sturm-Liouville方程,给出了耦合边界条件与分离边界条件下的特征值间不等式,利用自伴边界条件空间中一些边界条件的极限、自伴边界条件空间中的解析圈及连续特征值分支单调性的性质,证明了给出的不等式。

For a give Sturm-Liouville equation with change sign leading coefficient function,we give an inequalities among eigenvalues for coupled boundary conditions and those for separated boundary conditions.Using some limits on the space of self-adjoint boundary conditions,analytic loop of space of self-adjoint boundary conditions and monotonicity of continuous eigenvalue branch,we prove the inequalities.