A priori lower bound for the minimal eigenvalue of a Sturm-Liouville problem with boundary conditions of the second type

作者：Vladimirov A A^*; Karulina E S

来源：Mathematical Notes, 2015, 97(5-6): 846-853.

DOI：10.1134/S000143461505020X

• Sturm-Liouville problem
• infimum
• Lagrange finite-increment theorem
• minimal eigenvalue
• Holder's inequality
• the space L-gamma[0,1]
• gamma is an element of(0,1)

We establish the attainability of the infimum m (gamma) for the minimal eigenvalues of the boundary-value problems
-y'+qy=lambda y, y'(0)=y'(1)=0,
as the nonnegative potential q epsilon L-1[0, 1] ranges over the unit sphere of the space L-gamma[0, 1], where gamma epsilon (0, 1). We also establish that, for gamma <= 1 - 2 pi(-2), the equality m(gamma) = 1 holds and that, otherwise, the inequality m(gamma) < 1 is valid.

• 出版日期2015-5