Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees.
Nonlinear eigenvalue problems for fourth order ordinary differential equations
This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of...
Nonlinear eigenvalue problems with the parameter near resonance
Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.
Note on the absolutely continuous spectrum of Sturm-Liouville operators.