The Fucik spectrum of the discrete Dirichlet operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43951130" target="_blank" >RIV/49777513:23520/18:43951130 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2018.04.017" target="_blank" >http://dx.doi.org/10.1016/j.laa.2018.04.017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2018.04.017" target="_blank" >10.1016/j.laa.2018.04.017</a>

Result language
angličtina
Original language name
The Fucik spectrum of the discrete Dirichlet operator
Original language description
In this paper, we deal with the discrete Dirichlet operator of the second order and we investigate its Fučík spectrum, which consists of a finite number of algebraic curves. For each non-trivial Fučík curve, we are able to detect a finite number of its points, which are given explicitely. We provide the exact implicit description of all non-trivial Fučík curves in terms of Chebyshev polynomials of the second kind. Moreover, for each non-trivial Fučík curve, we give several different implicit descriptions, which differ in the level of depth of used nested functions. Our approach is based on the Möbius transformation and on the appropriate continuous extension of solutions of the discrete problem. Let us note that all presented descriptions of Fučík curves have the form of necessary and sufficient conditions. Finally, our approach can be also directly used in the case of difference operators of the second order with other local boundary conditions.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GA13-00863S" target="_blank" >GA13-00863S: Semilinear and Quasilinear Differential Equations: Existence and Multiplicity Results</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)