Theory of Vessels was started by M. Livšic in late 70’s as a part of more general theory, developed for n dimensional systems, defined by non self-adjoint commuting operators. In the Phd thesis of the author this theory is developed for the case n = 2 and there arise overdetermined time invariant systems and corresponding Vessels. A key idea of the construction is that transfer function of the ...

Surjectivity results of Fredholm alternative type are obtained for nonlinear operator equations of the form λT (x)−S(x) = f , where T is invertible, and T, S satisfy various types of homogeneity conditions. We are able to answer some questions left open by Fuč́ık, Nečas, Souček, and Souček. We employ the concept of an a-stably-solvable operator, related to nonlinear spectral theory methodology. ...

We consider a Sturm-Liouville boundary value problem in a bounded domain D of Rn. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on ∂D. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the me...

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

The paper summarizes the authors’ recent work on developing and proving an exponentially convergent numerical-analytical method (the FD-method) for solving Sturm-Liouville problems with a singular Legendre operator and a singular potential. It gives a concise general overview of the FD-method, outlines the proof of its convergence and exponential convergence rate when applied to the particular ...