25 research outputs found
The Jacobi operator on and its various -functions
We offer a detailed treatment of spectral and Weyl-Titchmarsh-Kodaira theory
for all self-adjoint Jacobi operator realizations of the differential
expression \begin{align*} \tau_{\alpha,\beta} = - (1-x)^{-\alpha}
(1+x)^{-\beta}(d/dx) \big((1-x)^{\alpha+1}(1+x)^{\beta+1}\big) (d/dx),& \\
\alpha, \beta \in \mathbb{R}, \; x \in (-1,1),& \end{align*} in
, . In addition to discussing the separated boundary conditions that
lead to Jacobi orthogonal polynomials as eigenfunctions in detail, we
exhaustively treat the case of coupled boundary conditions and illustrate the
latter with the help of the general -periodic and Krein--von Neumann
extensions. In particular, we treat all underlying Weyl-Titchmarsh-Kodaira and
Green's function induced -functions and revisit their Nevanlinna-Herglotz
property. We also consider connections to other differential operators
associated with orthogonal polynomials such as Laguerre, Gegenbauer, and
Chebyshev.Comment: 59 pages. arXiv admin note: text overlap with arXiv:2102.00685,
arXiv:2110.15913, arXiv:1910.1311
Asymmetric (p, 2)-equations with double resonance
We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian [a (p, 2)-equation] and with a reaction term, which is superlinear in the positive direction (without satisfying the Ambrosetti-Rabinowitz condition) and sublinear resonant in the negative direction. Resonance can also occur asymptotically at zero. So, we have a double resonance situation. Using variational methods based on the critical point theory and Morse theory (critical groups), we establish the existence of at least three nontrivial smooth solutions
Abstract book
Welcome at the International Conference on Differential and Difference Equations
& Applications 2015.
The main aim of this conference is to promote, encourage, cooperate, and bring
together researchers in the fields of differential and difference equations. All areas
of differential & difference equations will be represented with special emphasis on
applications. It will be mathematically enriching and socially exciting event.
List of registered participants consists of 169 persons from 45 countries.
The five-day scientific program runs from May 18 (Monday) till May 22, 2015
(Friday). It consists of invited lectures (plenary lectures and invited lectures in
sections) and contributed talks in the following areas:
Ordinary differential equations,
Partial differential equations,
Numerical methods and applications, other topics
Proceedings of the Workshop on Applications of Distributed System Theory to the Control of Large Space Structures
Two general themes in the control of large space structures are addressed: control theory for distributed parameter systems and distributed control for systems requiring spatially-distributed multipoint sensing and actuation. Topics include modeling and control, stabilization, and estimation and identification