Finite Spectrum of 2nth Order Boundary Value Problems with Transmission Conditions. (12th March 2023) - Li, Jia; Hao, Xiaoling; Li, Kun; Yao, Siqin
Abstract: For any positive integer 2 n and any positive integer m, l, a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most ( 2 n − 1 ) ( m + l + 1 ) + 1 eigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n ( m + l + 2 ) .