Localization of Fučík curves for the second order discrete Dirichlet operator

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43962114" target="_blank" >RIV/49777513:23520/21:43962114 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0007449721000701" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0007449721000701</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.bulsci.2021.103014" target="_blank" >10.1016/j.bulsci.2021.103014</a>

Result language
angličtina
Original language name
Localization of Fučík curves for the second order discrete Dirichlet operator
Original language description
In this paper, we deal with the second order difference equation with asymmetric nonlinearities on the integer lattice and we investigate the distribution of zeros for continuous extensions of positive semi-waves. The distance between two consecutive zeros of two different positive semi-waves depends not only on the parameters of the problem but also on the position of one of these zeros with respect to the integer lattice. We provide an explicit formula for this distance, which allows us to obtain a new simple implicit description of all non-trivial Fučík curves for the discrete Dirichlet operator. Moreover, for fixed parameters of the problem, we show that this distance is bounded and attains its global extrema that are explicitly described in terms of Chebyshev polynomials of the second kind. Finally, for each non-trivial Fučík curve, we provide suitable bounds by two curves with a simple description similar to the description of the first non-trivial Fučík curve.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-03253S" target="_blank" >GA18-03253S: Differential equations with special types of nonlinearities</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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