We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation , where α ∈ (0,1] and the functions are allowed to have singularities at the end points t = a, t = b of the interval under consideration.
The fundamental theory of existence, uniqueness and continuous differentiability of Lp-solutions for Neutral Functional Differential Equations is presented. Also, the spectrum of the solution operator of general autonomous linear NFDEs is described. Finally, an extension of Hartman Grobman Theorem on local conjugacy near a hyperbolic equilibrium is proved.
A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...
In this article, we consider the operator defined by the differential expression in , where is a complex valued function. Discussing the spectrum, we prove that has a finite number of eigenvalues and spectral singularities, if the condition holds. Later we investigate the properties of the principal functions corresponding to the eigenvalues and the spectral singularities.
For linear differential equations of the second order in the Jacobi form O. Borvka introduced a notion of dispersion. Here we generalize this notion to certain classes of linear differential equations of arbitrary order. Connection with Abel’s functional equation is derived. Relations between asymptotic behaviour of solutions of these equations and distribution of zeros of their solutions are also investigated.