Matrice de scattering et résonances associées à une orbite hétérocline
Matrix elements for sum of power-law potentials in quantum mechanic using generalized hypergeometric functions.
Maximum principles and uniqueness results of phi-Laplacian boundary value problems.
Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions
We consider Sturm-Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in L₂(0,1), except for some cases where this system is neither complete nor minimal.
Monomiality principle and eigenfunctions of differential operators.
Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string
In this paper we consider a parametric eigenvalue problem related to a vibrating string which is constructed out of two different materials. Using elementary analysis we show that the corresponding principal eigenvalue is increasing with respect to the parameter. Using a rearrangement technique we recapture a part of our main result, in case the difference between the densities of the two materials is sufficiently small. Finally, a simple numerical algorithm will be presented which will also provide...