The geometric multiplicity of each eigenvalue of a self-adjoint Sturm-Liouville problem is equal to its algebraic multiplicity. This is true for regular problems and for singular problems with limit-circle endpoints, including the case when the leading coefficient changes sign.

Abstract We prove local solvability and stability of the inverse Robin–Regge problem in general case, taking eigenvalue multiplicities into account. develop new approach based on reduction this to recovery Sturm–Liouville potential from Cauchy data

In this paper, we consider a non-homogeneous time–space-fractional telegraph equation in n-dimensions, which is obtained from the standard by replacing first- and second-order time derivatives Caputo fractional of corresponding orders, Laplacian operator Sturm–Liouville defined terms right left Riemann–Liouville derivatives. Using method separation variables, derive series representations solut...

‎In this manuscript‎, ‎we study various by uniqueness results for inverse spectral problems of Sturm--Liouville operators using three spectrum with a finite number of discontinuities at interior points which we impose the usual transmission conditions‎. ‎We consider both the cases of classical Robin and eigenparameter dependent boundary conditions.