Displaying similar documents to “Intertwining numbers; the n -rowed shapes”

Singular eigenvalue problems for second order linear ordinary differential equations

Árpád Elbert, Takaŝi Kusano, Manabu Naito (1998)

Archivum Mathematicum

Similarity:

We consider linear differential equations of the form ( p ( t ) x ' ) ' + λ q ( t ) x = 0 ( p ( t ) > 0 , q ( t ) > 0 ) ( A ) on an infinite interval [ a , ∞ ) and study the problem of finding those values of λ for which () has principal solutions x 0 ( t ; λ ) vanishing at t = a . This problem may well be called a singular eigenvalue problem, since requiring x 0 ( t ; λ ) to be a principal solution can be considered as a boundary condition at t = ∞ . Similarly to the regular eigenvalue problems for () on compact intervals, we can prove a theorem asserting that there exists a sequence { λ n } of eigenvalues...